Most of the heroes are at least slightly racist towards the Ishvalans. Edward Elric for instance, mocks their religion as childish nonsense.
The surviving Ishvalans have admitted that they hate Amestris and many of its people for what they did to Ishval. Many bluntly state that they may never forgive Amestris for what its people have done. However, most of them are willing to put this aside and work with the heroes to save Amestris because they want to end the cycle of unthinking hatred and vengeance.
Many of these refugees (they're all refugees) are motivated by the opposite side of Scar's religious position, that Ishvala would not want them to be consumed by revenge but to survive and carry on their culture and blood. This is almost the only truly positive depiction of religion among the many, many appearances and references it receives over the course of the series.
Miles, a soldier in the northern fortress of Briggs. Kimblee has a remarkable scene with Miles where he's flaunting his evil Ishvalan-slaughtering cred (he seems to have founded his whole identity there and gets a huge kick out of how much Scar hates him) and enjoying what he presumes is Miles forcibly restraining himself because of the chain of command, when really Miles has mostly made his peace with the genocide issue, values the living more, and just wishes the annoying guy would shut up, but won't say so because his job is to keep him busy.
Rorschach from Watchmen. He Does Not Like Women and is homophobic (both apparently the result of the abuses of his childhood that makes him recoil from any expression of sexuality), but he does try to do the right thing a lot of the time (albeit from his own effed up perspective). Similarly, earlier heroes Captain Metropolis and Hooded Justice, both seriously racist. (Not homophobic, though - in fact, they were a couple.)
Captain Nemo is a very rare non-white example. He harbors a severe hatred for the English but still works to save British civilians. Also shows a great deal of loyalty to his crew, many of whom happen to be white.
Walt Kowalski from Gran Torino, even toward the end of the movie after being adopted as a new grandparent by a Hmong family, still referred a particular Asian girl as "Yum Yum" when he couldn't pronounce her name.
Dirty Steve from Young Guns. He constantly harasses Chavez calling him a greaser and using Navaho as an insult, but in the final shootout he rides back to save Chavez getting himself killed instead. ( This also subverts the common, no longer racism because I was saved by a minority.)
The Rivers of War portrays Andrew Jackson like this. He is highly bigoted, even by the standards of the time, and does not hesitate to call friendly Cherokees "savages", ask how Sam Houston can be so sure that his coloured teamsters won't steal his gear and sum up state militias as drunken and cowardly to a man. However, he hesitates to shoot Red Eagle (a rebel Cherokee responsible for a major massacre) because he surrendered voluntarily, promotes a coloured sergeant to commissioned rank, against regulations, and threatens to kill a man who protests against arming free coloured men, but who won't join the militia himself. Essentially, the Andrew Jackson in the book is bigoted against groups but is capable of respecting an individual who is especially heroic and or a fierce fighter. While he is a bigot, he hates fools and cowards even more.
Played for laughs in Good Omens with Witchhunter Shadwell. He has a (mildly) derogatory slur for everyone, belittles foreign cultures and religions, and suspects everyone of being a witch or a warlock, yet everyone is charmed by him and he fearlessly prepares to fight Satan when the Apocalypse comes.
He also (maybe) acknowledges that Lady Margolotta (a vampire) isn't a complete monster (though he doesn't like her), and highly values Angua (a werewolf), Detritus (a troll), Cheery (a dwarf), and all the other Watchmen he works with, because they're no longer just dwarves/trolls/werewolves/vampires...they're watchmen.
In return, the non-human members of the Watch generally ignore Vimes' racist rhetoric, because they know that if their backs are against the wall, he'll be the first one diving in to help them.
Albrecht Albrechtsson from The Fifth Elephant hates Ankh-Morpork, but he's a good, loyal dwarf who, Rhys notes, probably would have made an excellent king a few hundred years ago.
In the Dragaera universe, the Vlad Taltos books give us Aliera, and sometimes Vlad himself. Played with and lampshaded by Vlad when he realizes that, while he hates Dragaerans, almost all his friends and loved ones are Dragaerans.
Slughorn in Harry Potter is a minor example. While he's one of the most sympathetic characters Slytherin House produces, there are times when he displays the 'Blood Purity' ideology that makes most Slytherins so distasteful; he assumes Voldemort must be a pure-blood due to his immense magical power, and expresses mild surprise when he finds muggle-born wizards with above-average talent, such as Lily or Hermione. His final opinion of a person will always be based on their talent, however, and he won't look down on a muggleborn for long if they manage to impress him.
In The Grimnoir Chronicles, Joe Vierra is a Portuguese farmer who spits at the Okies that pass by his farm. But he still buys and adopts the daughter of one family when he notices that she has a potentially self-destructive power that needs training.
Isengrim from The Reynard Cycle is portrayed this way consistently, in spite of the fact that he's rejected the society that made him that way. Old habits die hard, apparently.
Barrayar in Vorkosigan Saga. Honorable and valiant warriors who always keep their word but have an extreme prejudice against cripples.
In Tom Kratman's Caliphate, Adbul Mohsem might be anti-American, but he did care about Petra's well-being unlike his wife Khalifa.
Lord David Alderscroft, from the Elemental Masters novels, isn't quite as bad as some of the other examples on this page. But in most of his appearances, he assumes that nonwhites, the lower (social) classes, and females are inherently inferior to wealthy, white male nobility like himself.
Angel: Connor was brought up to hate demons and magic by the Obliviously Evil Holtz, but has no intention of hurting humans (at first). Wesley even uses this as an excuse for not cluing Fred and Gunn in about him in "Deep Down".
Andy Sipowicz from NYPD Blue is a reformed mean drunk, whose racial bigotry stems ostensibly from his father being battered by a black man when trying to read the man's gas meter, and his own experiences infiltrating the Black Panthers when he was still freshly traumatized by his Vietnam war experiences. Sipowicz struggles to keep his racial bigotry from affecting his work, and consistently displays genuine empathy for people of color, even though at times his temper gets the best of him and he says the wrong thing to the wrong person.
Logan Echolls from Veronica Mars is something of a racist, and very much a classist. He really hates poor people. And yet, he's also genuinely heroic at times, and we root for him, and we cheer when he falls in love with Veronica and they become a couple.
Daryl Dixon from The Walking Dead. While he still harbors the same racist tendencies as his older brother Merle and makes wisecracks about "Chinamen" at the end of the day, he's still an effective and capable survivor who's a crack shot with both a crossbow and rifle, and he pitches in to help the rest of the survivors as much as he can.
House: Gregory House: He's bigoted toward everyone but he will do whatever it takes to save their life from whatever disease is killing them. Four or more ethnic subtypes have worked for him and he mocks them equally. It's lampshaded in one episode after he fails to ruffle Cameron's feathers; she tells him that he's "a misanthrope, not a misogynist." Other times he makes racist and sexist comments because he likes to annoy people.
Frances "Our Country, Our Rules" O'Brien from The Librarians. In spite of her frequently culturally insensitive comments and racially stereotyping (thinking that an Arabic internet banking site was advocating terrorism), she still manages to work with and even apparently care about a highly diverse group (many of whom she presumably does have the authority to fire). She's made more sympathetic by her unfortunate home life, her past, her panic disorder and the fact that at least some of her behaviour is apparently resultant from her repressive Catholic upbringing (diving into Christine's breasts obviously suggested she did still have at least some bisexual leanings she was denying).
Rafe McAuley from Defiance. He generally hpold aliens, especially Catithi in contempt, largely because of the war but he also tries to do the right thing, even, eventually, coming around, more or less, to his daughter marrying a Castithi.
Warhammer's High Elves are virtually all Noble Bigots, being incredibly haughty, aristocratic and condescending towards all non-elves, but at the same time devoted to fighting the forces of Chaos and protecting the world and its people from destruction. The entire elven race is afflicted with a sense of its own superiority over everyone else, but where this causes the Dark Elves to despise and enslave others and the Wood Elves to ignore them, in the High Elves it manifests as a patronising tendency towards helping the poor "lesser" races who couldn't possibly survive without High Elf help. One or two High Elves are aware of their racial prejudices - Teclis for instance - but most see it as the natural order of things. That elvenkind is naturally gifted far beyond the race of man provides a foundation for their monstrous egos.
*Mute from the visual novel Analogue: A Hate Story is extremely open about her sexism and homophobia, yet shows compassion and even admiration for actual women and lesbians, if heavily filtered by her prejudices. In Hate Plus in the aftermath of *Mute's suicide you learn that her original, factory-state programming has no such bigoted ideas—they were very much taught and in large part literally programmed by the patriarchal Ryu dynasty.
Zelos Wilder from Tales of Symphonia was taught from birth that half-elves were disgusting, stupid, beneath regular humans, saw his mother get killed by a half elf and confesses to the rest of the party that he feels conflicted about traveling with two half-elves. However, at the same time, he sympathizes with them far more than he does with his aristocratic background, and even before meeting the party, he stopped the Pope from passing various anti-half-elf legislation.
It'd be quicker to list the Mass Effect characters who don't fall into this. Almost every one of your squadmates will have at least moment of mistrust, condescension or downright hostility to some other species. Fans tend to point to Ashley as the "racist" squadmate, but she's one of the milder cases - she just worries about letting alien nationals (including a bounty hunter and a Cowboy Cop) on your prototype warship and believes that the Council will sacrifice humanity when times are difficult. The kicker is when Dr. Chakwas, ship medic and all-around Cool Old Lady, reveals some unexpectedly strong feelings about synthetic life in the third game.
The bigger kicker is if you disagree with her, she dismisses it and calls you a machine due to Shepard's cybernetics.
Khelgar Ironfist from Neverwinter Nights 2. Initally hates Neeshka because she's a tiefling. Hates Elanee because she's an elf. Through his sidequest though you can get him to see his attitudes are an injustice. If you complete that quest he never quite forget them but he far more willing to let the person's actions speak.
Jarl Ulfric Stormcloak of The Elder Scrolls V: Skyrim is a Fantastic Racist who places the rights of the indigenous Nords above those of the immigrant Dunmer, Argonians and Khajiit, but ultimately recognises that loyalty is more important than blood and will allow non-Nords to serve in his army if he's convinced they are loyal to Skyrim and his ideals.
Dennis Vicarth in Front Mission 3 made a few off-color remarks about the Japanese but is still willing to help Kazuki.
The Elven hero Nasrudin in Arcanum. Founded the Elven Council, devoted much of his life to righting wrongs and fighting evil, and became the inspiration for the Panarii religion... at the same time, an arrogant supremacist who was motivated to heroics by a belief that elves were the greatest, wisest race, and who felt it was his duty to act as shepherd and protector toward what he regarded as 'lesser races.'
Wakka from "Final Fantasy X" was a fun-loving, easy-going joker of a Big Brother figure to many in the party. He was also a devout Yevonite during the first half of the game and shared the religion's condemnation of the machina-using Al Bhed. He makes numerous disparaging remarks about the Al Bhed throughout the game, all the while looking out for his "little sister" Yuna, who is half Al Bhed. He later befriends Yuna's Al Bhed cousin Rikku. He's horrified to learn that both have Al Bhed heritage but eventually overcomes his prejudice and apologizes for his previously bigoted attitude.
Guilio from Gungnir is quite racist against everyone the same race as his oppressors. There are also a few women on Guilio's side that see his race as nothing more than tools to be used.
Maribelle from Fire Emblem Awakening, who is the daughter of a duke, holds some prejudice towards those of lower social class, which she speaks of constantly even to her lower class allies, even when she is trying to assist them in some way.
Rico from Killzone hates the Helghast for invading his planet and wiping out his unit and never misses an occasion to remind it to everybody, but especially to his half-Helghan teammate Hakha. He changes over the course of the first game by slowly warming up to Hakha and even taking a bullet for him while fleeing the SD platform. In the second game, it's clear he still loathes them, but went from Kill 'em All to spare a civilian Helghast in the second game and being as horrified as everyone when their planet is nuker in the third game.
Dominic Deegan Siggy was this briefly.note Briefly refers to the Noble part of the equation; bigotry is always there.
Equius of Homestuck is an alien version. He's contemptuous of his fellow trolls with blood colors too far to the red end of the rainbow and annoyed that the more purple-blooded Gamzee doesn't act like an aristocrat. He's also perfectly willing to work with lesser-blood trolls and even makes a pair of robotic legs for one on the bottom of the totem pole. His bigotry ends up getting him killed when Gamzee goes on a murderous rampage. Despite his obscene strength, he doesn't lift a finger to defend himself.
Rudy of Kevin & Kell, while a Jerk with a Heart of Gold, has problems accepting an herbivore as his stepfather and the head of the family, yet gradually grows closer to Kevin over time, even making an anonymous call exposing himself as domesticated (a condition he finds deeply shameful) to Kevin's insurance agency so that Kevin won't lose his insurance. Even Kell, despite being in a Maligned Mixed Marriage, has some prejudice against felines; an arc focuses on her working on those prejudices.
Cartman in South Park, surprisingly, is turning into this in the most recent seasons. After his scary encounter with "Jewpacabra" and subsequent proclaimed conversion to Judaism he argues in favor of an angry and malicious Torah/Old Testament god. And the entire plot of "Cartman Finds Love" revolves around his racist views manifesting in a need to hook Token up with the new black girl in class because they 'belong together'. The lengths he goes to prevent Kyle from mucking up is plan is pretty extraordinary.
The Teen Titans episode "Troq" featured Val-Yor, an intergalactic space hero who enlists the Titans' help to defeat an otherworldly menace. Unfortunately, his people are extremely prejudiced against Starfire's people, and he repeatedly uses the slur "Troq" (meaning "nothing") when speaking to her. He gets along so well with the other titans (green-skinned elf boy, demon girl, black cyborg, and the Token Human) that they think "Trog" is a harmless term until she corrects them. He ultimately parts with the Titans on chilly terms.
Pakku held sexist values for most of his life. When he was a teenager, his bigotry caused his fiancée Kanna note Katara's future grandmother to leave him. After realizing this as an old man, he realizes that his ideas were wrong and starts to see women as equals. (For example, he trains Katara in combat waterbending and admits that she's equal or better than his male students.) He meets up with Kanna again, and after she realizes that he's changed, she marries him, making him the grandfather of Sokka and Katara.
Sokka is a bit sexist for the first few episodes, believing that women should Stay in the Kitchen and out of the fighting. After getting to know a group of female warriors firsthand and realizing their fighting capabilities, he realizes that his views were incorrect and learns to respect women and girls. After that it's gone.
A lot of characters in ThunderCats (2011) are this to some extent, most notably Tygra and Claudus, and the Cats in general.
Claudus cares about and does a good job of ensuring the safety and well being of his people and Tygra has a good heart underneath his jerkish exterior, but both have a distinct dislike of Lizards, and Tygra holds a bad opinion of Dogs. These beliefs are common for most of the Cats living in Thundera though due to generations of conflict between the two.
One reason Lion-O is considered weird is that he's not a bigot at all, noble or otherwise.