Granted, the science side in this series isn't any better...
In Fullmetal Alchemist (bothversions) Ed and Al travels to a town where everyone except for the leader of the Corrupt Church runs on this trope. Such as blindly following a manipulative con artist, and when he disappears, going violent and destroying everything (which may not have been the conman's intention, but certainly was that of those who put him in power).
The manga and Brotherhood series as a whole subverts the trope, however, as it takes Ed the entirety of the series to figure out the truth behind... erm... Truth.
The religious fanatics in "Bio Apocalypse" take this trope to the extreme.
Termight Empire in Nemesis the Warlock are religious fanatics seeing aliens as demons, worshipping clearly insane leader as a God and getting themselves killed with undying fanatism. Nemesis' battlecry is Credo! (Believe in latin) but he points out he means it like "belive in yourself".
Agora, focusing on the death of the philosopher Hypatia, depicts Christians as fanatical assholes, in which their fanaticism is raised Up to Eleven thanks to the sheer intolerance towards pagans and Jews; the "stupid" part of the trope comes from the fact their intolerance blinds them to the point of stupidity, attacking at random with disastrous consequences. The accounts used comes from pagan writer Damascius (who were enemies with the Christians) and Edward Gibbon (a strong atheist).
Monty Python's Life of Brian depicts religious believers as stupid at a number of points, refusing to think for themselves and fracturing off into sects divided by trivialities. The Jewish revolutionary organizations and the followers of Brian are both examples.
When Everett witnesses a riverside baptism service, he comments: "Well, I guess hard times flush out the chumps; everybody's lookin' for answers."
After Everett's travel companions get baptized themselves, Everett remarks; "Baptism! You two are dumber than a bag of hammers."
Toward the end of the film, when facing his own death, Everett falls on his knees and repents of his sins before God. After he is delivered from death (thanks to a sudden and massive flood of water), Everett discounts his conversion by noting that "any human being will cast about in a moment of stress." When his companions proclaim that the flood was an act of God, Everett comments, "Again, you hayseeds are showin' your want for intellect." (Note: Everett's watery salvation functions as a clever twist on Death by Irony. Deliverance by Irony, perhaps?)
There is a take on this trope in My Father My Lord. Although the deeply pious father is shown to have a slightly negative impact on his wife and son because of his devotion to Judaism at first, his faith ultimately is shown to have tragic consequences; a day taking his son Menachem to the Red Sea, whilst his father and the other devotees are lost in fervent prayer, he slips away into the water and drowns. His father's love for the unseen trumped his fatherly duties to keep watch over his son.
Inverted in Foundation, where the huge difference of technological development between The Foundation and their neighbours leads to a religion when the Foundation tries to share their knowledge with them. This happened because it was the only way their neighbors would have accepted their technology (which they saw as sorcery).
Dune. Anyone order a thousand years of Holy Wars that nearly sent interstellar travel down the tubes? The setting specifically examines the issue of how a large populace interprets the words and deeds of a religious prophet who spoke and acted for a specific place and time. In truth the prophet(s) eventually managed to accomplish what they set out to do, human physiology and psychology advanced, and human society became more modern, peaceful, and diplomatic. Then the Bene Gesserit and Honored Matres decide to get into a fight over who can better use hypno-sex to control populations, and things get messy.
Which was in turn a reflection of the author's beliefs about organised religion in general. It appears to be mostly an attack on Christianity, but that's due to him growing up in a predominantly Christian country.
That's not so much Belief Makes You Stupid as Belief Makes You Evil And Dogmatic, considering that the Magisterium are intelligent and dangerous antagonists.
In his nonfiction, Robert Anton Wilson of Illuminatus! fame has declared, in direct quote that "Belief is the death of intelligence. As soon as one believes a doctrine of any sort, or assumes certitude, one stops thinking about that aspect of existence." Notably he includes dogmatic science (as opposed to progressive science) under the definition, as well. The theme of free-thinkers who dare to question the "obvious" values and beliefs of their society is constant in all his novels.
The Sword Of Truth holds that both belief and emotion make you stupid. So a character who claims he has faith in his feelings must be quite insane. Mind you, characters claiming this have been known to make some rather impressive intuitive leaps themselves.
Religious people in Neal Stephenson's Anathem run the full gamut of stupid, from trying to murder a guy who saved one of their members' lives to believing that strange lights in the sky are a sign that the world is going to be judged. (The work also provides numerous examples of not-stupid religious people.)
Although the Discworld novels criticize organized religion much more than belief itself, the third The Science of Discworld book, Darwin's Watch, employs this trope somewhat.
"Somewhat" in this case meaning "If Darwin hadn't written Origin of the Species, humanity would never leave the planet before it froze."
He doesn't just not write it; he writes a book just as convincing in the other direction and more or less ends science.
Subverted in Tom's Midnight Garden. Abel, the pious caretaker, at first appears to be a superstitious ignoramus, who thinks Tom is a demon; eventually, his belief allows him to recognize that Tom isn't evil. Later, as discussed in a conversation between Hatty Bartholomew and Tom, the fact that Abel could see Tom strongly implies that he was far more perceptive than anyone gave him credit for.
In The Pale King, Chris Fogle had nothing but contempt for his religious roommate and his girlfriend.
Subverted in the Book Of The Long Sun. Patera Silk's religion and gods are false, but there are facets of truth behind the lies. Silk manages to be a great leader in spite of it.
Father Brownís general appearance made him look dumb to everyone, but this trope is continually applied to him by his condition of Catholic Priest: A lot of people in his stories (The Blue Cross, The Flying Stars, The Hammer of God, The eye of Apollo) constantly make the wrong assumption that a priest is a celibate simpleton unaware of the Real Life. In fact, a priest must study philosophy and theology precisely to defend his beliefs helped by logic, and the fact of hearing a lot of people confessing his sins give him an interesting perspective about Real Life. Lampshaded in The Blue Cross when he explains to Master of DisguiseGentleman Thief Flambeau how he discovered him:
"How in blazes do you know all these horrors?" cried Flambeau.
In Good Omens, most of humanity appears this way. Best shown when Aziraphale gets accidentally exorcised by Shadwell and spends the next several hours body-surfing around the aether, causing nearly everyone he encounters to assume they're being inhabited by a Demon. With slight irritation, Aziraphale has to correct them that he's actually an Angel.
Aziraphale also terrifies an televangelist and his congregation for the ludicrous notion of the Rapture, pointing out that during the Final Battle, the Angels fighting in the Celestial War will simply be too busy fighting the forces of Hell to go around picking random people up. Between the Heavenly War and the War down on Earth, any human that dies in the crossfire will be considered acceptable civilian casualties and it's up to God to clean that mess up... And that's if they actually win!
It's not really belief in general, it's just that that specific aspect (which is pretty much unique to American evangelicals) happens to be wrong.
In Wicked, Nessarose Thropp is a religious fanatic whose contributions to conversation are often not wanted and perceived by whoever is narrating as narrow-minded or too innocent.
In Glow by Amy Kathleen Ryan, Waverly has this belief about religion, even though she is dating the highly religious Kieran. When she and all the girls on her Generation Ship, the Empyrean, are kidnapped by their sister ship, she distrusts their zealous captain, Pastor Anne Mather. Later, when she sees the same tendencies in Kieran, who has taken over the Empyrean after the death of the captain, she automatically distrusts him and all his followers.
Live Action TV
Star Trek, at least until Deep Space Nine fleshed out the Bajorans as more than spiritual cannon fodder for the Cardassians.
The Babylon 5 episode "Believers" depicts a family from a zealously religious species refusing to allow Dr. Franklin perform simple life-saving surgery on their son because their religion states that he will lose his spirit if he is cut open. The alien parents are earnest and loving, but their arguments are little more than strawmen, and their culture is depicted as insular and close-minded at every turn. Franklin's belief that Science is superior to Religion fits this trope as well, right up to the point where he saves the child, expecting the parents to turn around and realize he was right, only to have the wind taken out of his self-righteous sails when the parents kill their own child, believing him to be effectively a soulless zombie. In the end, the episode leaves who was right and who was wrong ambiguous and up to the viewer to decide.
The episode "Confession and Lamentations" is much less ambiguous: the Markab race is plagued by Drafa, an airborne disease 100% contagious and 100% lethal, and due the widespread belief of it being a divine punishment for immorality the Markab failed to take the appropriate precautions, even forbidding the few Markab who believed it just a deadly disease from enlisting help from non-Markab and negating funds to study it. In the end Franklin manages to find a vaccine and a cure thanks to Lazarenn (a Markab doctor on the station) becoming ill and sacrificing himself to allow him to study the illness, but by then the entire Markab population on the station is dead, and the losses among the wider Markab population are so great that the race is not genetically viable anymore, dooming it to die out in a few generations.
On Lost, Richard Alpert is Catholic, and, in 1867, he accidentally kills a man while getting medicine for his dying wife, gets arrested, is told he can't be absolved for his sins, and then crashes on the island. Naturally, he is willing to believe he's gone to hell when told just that by an apparition of his dead wife and a mysterious Man in Black. Exploiting Richard's faith, the Man in Black tells him he can only escape "hell" by killing "the devil," the Man in Black's archenemy Jacob. The plan falls through when Jacob explains Richard is not dead, not in hell, and was misled by the Man in Black.
A staple of classic Doctor Who. Religion was usually portrayed as the antithesis of science and any character fanatically loyal to a 'god' and doing things in 'his' name would ultimately be revealed to be deluded and worshipping a mad computer (Face of Evil), an empty spacesuit (Planet of Fire), etc.
Modern Doctor Who has used this and its opposite, but an example of the trope being played straight would be The Doctor's Daughter, where the soldiers' deity turns out to be a terraforming device.
Averted on The X-Files, of all shows. Though the premise of aliens and the paranormal may seem like the antithesis of religion (as it's usually portrayed), religion gets a ton of screen time during the series. Besides the Monster of the Week episodes that deal with things like stigmata, demonic possession, and recordings made by Christ, the show has a lot of religious undertones. However, these undertones aren't "God is responsible for everything on the show" kind of things. More questioning religion and how it came to be. At one point, Scully finds an extraterrestrial engraving that contains passages from the Bible, and Scully herself experiences a birthing experience similar to the birth of Christ. This interplay of religion and science also plays large role in Scully's character development. Though a skeptic of Mulder's theories, she is a practicing Catholic and often must reconcile what she's learning with her faith.
Played straight in earlier seasons, however. Mulder does everything but call Scully an idiot for her belief. It comes out horribly, however, as up to this point, Mulder has yet to come up with any significant proof for his own theories. And someone who believes in spirits and some sort of afterlife who criticizes the religious will always seem a bit silly.
Scully calls Mulder out on this several times.
Somewhat subverted in Lewis, with DS James Hathaway being an ex-seminary student, and also incredibly smart. Played Straight when he reveals his involvement in the suicide case of "Life Born of Fire" He told his gay friend that God couldn't love him as he was, starting the chain of events that led to his suicide
Hathaway: Have you ever been so sure you were right and then you look back and you can't believe what you thought? I was training to be a priest! It was so exciting. I was surrounded by people who thought just like me and I thought just like them! But these things they say, it's so easy. Like breathing, you just believe it and I believed!
"Creepy Steve" in the Character Blog series KateModern is blissfully unaware of the criminal actions of the Hymn of One.
The Adeptus Mechanicus of Warhammer 40000 believe that all knowledge already exists, and that it must be found from ruins of the past rather than sought out—in this case, they're right, because the majority of human technological prowess was lost during the Age of Strife, and they're trying to recover it from various Forge Worlds. They tend to call any new technologies, human or alien, heresy unless they can be called a 'modification' of an existing STC technology. The Predator Annihilator is a well known example of this.
Warhammer 40000 universe plays with this trope, because there is actually little space for a belief. All tenets of religion (existence of God-Emperor and ruinous powers of Chaos to name the few) are based on facts. The members of clergy (especially members of Inquisition and Adeptus Mechanicus) are usually the best educated people around.
The Eberron setting is deliberately vague about whether most of its gods "really" exist or not. It's not even slightly vague about the fact that in practical terms it doesn't matter; everyone goes to the same place when they die at least in the short (cosmologically speaking) term, and clerics of all faiths, even the ones that mutually contradict each other, get clerical spells. Any "Commune with Deity" type spells get you something like an archangel instead, who, if really pressed on the issue, may admit they've never actually seen the gods either. There are several established faiths, but a cleric who really wants to can devote himself to an ideal or concept instead with no penalties (some of the established faiths have prestige classes with special abilities, for which you must be a member of that faith, but all regular clerical spells work just fine for any cleric).
Adopting general policies related to theocratic government often slows down your researching ability (generally either halving the rate or stopping Libraries, Universities, etc. from applying bonuses). The tradeoff is faith-empowered troops and cheaper (if not outright free) variants thereof, along with marginally happier citizens (or in Civ II, no unhappy citizens at all).
In general, each of the seven religions serves as merely a diplomatic modifier, encouraging alliances between empires of the same religion and directing animosity towards the heathens that dare to worship some other deity. The difference is almost entirely cosmetic, and the only reason conflict even comes about is because the AI is programmed to automatically hate empires of different religions. In multiplayer games, religion is a non-factor in deciding allies and enemies. In this case, Belief Makes The AI Stupid(er).
Religious governments do not receive any penalty to research, but a government with the "Free Religion" civic, which cancels out the government's religious affiliation, grants a bonus to research. However, the game also rewards religious diversity (i.e. spreading multiple religions), especially since Free Religion gives better bonuses the more religions you have in your empire, and the natural setting is paganism, so there is no 'state atheism' setting, despite the presence of Communism and State Property. Additionally, Monasteries (which are available to all religions) grant nice early research bonuses.
Also subverted with Sister Miriam's in-game bio and quotes: While she's definitely wary of technological advancement, she hardly thinks that Science Is Bad (at least, not at first). She is also a trained psychologist and (like all of the leaders) has a deep, philosophical reason for her concerns. Miriam seems to have read and understood Dostoyevsky, to some degree—not scientific, but not stupid either.
The GURPS roleplaying supplement examines it further: The best and brightest in Believer society are more likely to become theologians than scientists, and new technology has to be vetted by the Moral Guardians for approved uses before it becomes commonplace.
Ironically, this trope was useful in Civ 2: The theocracy was inept when it came to scientific advancement, but the religious fervor made every citizen satisfied with his life and it was the best kind of regime to win war: Jumping from democracy in times of peace to theocracy in times of war and back to democracy once the war was won was a very efficient strategy (for beginners, at any rate).
In the DS version of Revolution, this trope is played straight and inverted. The closest thing to a theocracy is the 'Fundamentalism' government type, whereby cities abandon scientific study for the sake of culture. However, religion in general actually improves scientific advancement by giving you access to technology like the printing press.
Europa Universalis, though not a Sid Meier game, features a slider that dictates the church's activities: one side puts focus towards the arts, humanities, and sciences, while the other side focuses on missionary and conversion efforts. Interestingly, a later patch popular Game Mod renamed the slider from "Innovation vs. Narrowmindedness" to the more even-handed "Innovation vs. Tradition" to emphasize the fact that both sides are equally viable choices depending on the player's strategy, making it less a case of Belief Makes You Stupid than Conservatism Makes You Conservative.
Which religion you culture belongs to can have a bigger effect. There's your choice of state religion, and your religious/cultural 'tech group'. Catholics and Protestants share a 'latin' tech group, the best, but Reformed>Protestant>Catholic>Counter-reformed, and so on. Because of the game's time period, there is strictly speaking no 'no belief' setting to make you 'less stupid'.
The Covenant of Halo hold Forerunner technology as religious artifacts. They simply copy the artifacts as they are, and it is considered heresy to change or improve on them in any way, shape, or form. Ironically, despite being leaps and bounds ahead of humanity technologically, their mathematics are way behind, as all they do is copy. When humans get hold of Covenant/Forerunner technology and apply the superior mathematics, it is far more powerful than anything the Covenant make.
In one of the books Cortana got better effects from a captured ship's engines and weapons simply by fiddling with the settings.
In The Elder Scrolls IV Oblivion, while it's certainly true most of the priests are decent people and the gods are mostly benevolent, the Church itself participates in mass censorship, oppressed the necromancers into demon-worship thereby creating one of the Big Bads of the series, and perpetrated the genocide of the Ayleid.
In the other The Elder Scrolls games, it's played with. The way the story is told (player perspective only) and the way said player receives information about the religions (other character perspectives only) most religions claim this about most other religions.
Of course, one must consider that Necromancy by it's very nature is considered an abomination by law abiding magicka users, and that by all accounts the Ayleids were pretty big dicks.
Tales Of The Abyss is a subversion. The intelligent, level-headed followers of the Order of Lorelei (ie: Tear and Ion) are on the side of good. The Knight Templars like Mohs, on the other hand...
Although, as it turns out, said characters are trying to destroy the aforementioned deity-equivalent.
Dead Space gives us Unitology, a religion that preaches oneness of all humanity, but only after death. They also don't reveal the whole Necromoprh mutation thing except to their most exclusive members, i.e. the ones that have paid the most money and are thus the most loyal.
Shin Megami Tensei's Messians and Gaians. Ye gods. Both, while having many, many good points in favor of their own sides. Still, their favorite method of conversion is essentially beating the other side to death while proclaiming their superiority. Even their ownleaders don't think that highly of them.
Inverted in Immortal Souls, to an almost exaggerated degree. The Templars are by far the most technologically advanced group in the setting, having Power Armor, Energy Weapons, and the like in what is otherwise a present-day setting, presumably so they as squishy humans can hope to match the powerful supernatural monsters they fight. They also engage in Mad Scientist-esque scientific research on said monsters. Lampshaded at one point when their leader boasts they'll succeed "thanks to our advanced technology and superior divine right".
Demon's Souls' treatment of this is quite interesting. Magic is treated by some Sages (notably Sage Freke) as something quasi-scientific, while Faith is reserved for the masses, led by a saint. While Urbain's followers (especially that one person in the corner that does nothing but moans his fate without doing anything) and Urbain himself is shown to be a bit thick and detached with the reality and the identity of the god they worship, Saint Urbain did subtly recognize that the main Big Bad, The Old One isn't a large cosmic Eldritch Abomination everyone make it out to be. On the other hand, magic isn't as straight out scientific as Freke analyzed (what with Yuria's witchcraft having an element of chaos to it). This, coupled with Freke's reversal of attitude at the end of the game (that is, from "what does Souls' relation to magic" to For Magic!) means that, if Belief Makes You Stupid, Naytheism Makes You Power Hungry.
In strictly game terms however, Faith is the only thing that increases your Magic Defense, firmly establishing the Magic Versus Faith theme.
In this strip of Tales of the Questor one person indicates that the religion "Does not takes kindly to ideas— or thinking — not their own crafting" The pauses are probably intentional. He also indicates his job is to deal with anything that might threaten or challenge his masters beliefs in any way. It is a reoccurring issue in the comic that humans, partly because of religion, cannot deal with the concept of 'Lux energies' and insist on calling it magic, and with magic being evil to them...
Thoroughly averted, though, with the more religious of his racconans, whose beliefs spark compassion.
Rather obviously Catholic vs. Protestant, with the strawman religion being Catholicism. (The churches are called Sojourners' and Universal (Catholic means universal) and the use of symbols, architecture, etc, suggests the parallel also.)
Tamago in Negamaki! causes zig-zagging with this trope. He's overtly religious and profoundly stupid about it but when Chief Buffalo Jerky asks if all religious people are like him, Negamaki cites the many positive aspects of having a religious conviction; Tamago would be that stupid without one.
South Park's general philosophy towards religion seems to be "faith may make you stupid sometimes, but it will probably also make you good (or at least well-meaning)." The episode "All About the Mormons?" especially plays with this; the Mormon family is presented as ridiculously gullible for buying the story of how their religion was founded, but when Stan calls them out for that one of their sons points out that they're also the only family in the entire town who's happy and loving, largely because their church's main focus is on family values, not religious history.
Then they still got it a bit off, as the history of the church is a major focus of study (alternating with books of scripture). The origin story is seen as vitally important, as it's the thing the LDS church bases its validity on. *
For example, if Joseph Smith didn't have the First Vision and the Book of Mormon is a hoax, then there goes the keystone of a member's testimony that their faith is God's restored church.
The Simpsons seems to lean this way in recent seasons, as Ned has gotten Flanderized from "overly religious Good Samaritan" to "The FundamentalistKnight Templar", usually so he can be arrayed against the more scientifically-minded Lisa. In "The Monkey Suit", Ned's opposition to the teaching of evolution turns the town into a fundamentalist dystopia, and in "You Kent Always Say What You Want" he went on a crusade to cleanse television after Kent Brockman swore in pain upon taking some hot coffee to the lap*
And before that, we see Ned monitoring all TV shows for "impropriety", including Krypto "licking himself" on Smallville, prompting even his own children to say You Need to Get Laid
. Other characters who are on the religious side, such as Rev. Lovejoy, Helen, etc. become Fundamentalists, solely supporting religion and rejecting anything that contradicts or attempts to contradict.
Like the game, this is almost played straight in Dead Space Downfall. Nearly all the Unitologists are shown as either ignorant, horrible misguided, violent lunatics, and even just plain not right in the head. The biggest exception is Samuel Irons who is portrayed as being the Only Sane Man among the entire Unitologist sect, as he is clearly aware that the Marker and necromorphs are a threat rather than as a key to ascension. Not only does he help the initially distrustful Doomed Protagonist Alissa Vincent and her P.C.S.I. Security team cut down the horde of undead marauders, he performs a Heroic Sacrifice by distracting the necromorphs so that Alissa and her remaining team member helped the survivors escape (which all go in vain of course).
In Avatar The Last Airbender, a village's blind faith in a fortune-teller nearly gets them all killed. Even Katara, who is often a voice of reason, falls victim to this trope, and asks for huge numbers of ridiculously specific predictions; at one point she asks if she should have a mango or papaya for breakfast the next day, (and on being exasperatedly told the latter, she goes and buys one, even though she hates papayas). However, in a slight zig-zag, while the many flaws in their logic are pointed out by Sokka, (who gets completely ignored,) none of the predictions actually turn out to be wrong, even though they require the Gaang's direct intervention to turn out right. Most of them, however, were of the Self-Fulfilling Prophecy variety (like the guy she told he would meet the love of his life while wearing red shoes, so he started wearing them every day), nobody in the village seems to understand the logic behind this when Sokka tries to explain it.