Prime Minister Wong in Mobile Fighter G Gundam is portrayed this way in his first appearances. Cheerful, friendly, applauding the hero's victories and inviting him to his penthouse for a drink, he's a stark counterpart to Master Asia. And then it's revealed he's a villain and he rapidly stops applauding Domon and starts rigging the matches to get him killed.
Detective Ooishi from Higurashi: When They Cry borderlines between this and Agent Mulder. He's always searching for clues as to the cause of the string of murders and takes any useful information, but is considered too obsessive over the topic and has been urged to step off the case a few times.
Dr. Irie might be a straighter example from the same series. Except for the whole, you know, paedophilia thing, and even that might be a joke. The problem is, once he figures out what's going on it's not always to the benefit of the person telling him what's going on.
Keiichi's father, Ichiro Maebara (who only really consistently appears in the manga) is this, to a much lesser extent than the above. He fully supports Keiichi's efforts in Satoko, regardless the fallout his family faces; on the other hand, he also makes sure to let Keiichi know that he should not resort to violence to save his friend and instead handle it the right way.
The Time-Space Administration Bureau at the start of Lyrical Nanoha is a surprisingly understanding and helpful instance of The Federation. They're perfectly willing to cooperate with the heroine even though she's Just a Kid (it helps that Midchilda apparently lacks age of majority or child labor laws) and are quite understanding of the franchise's numerous Anti-Villains. Lindy Harlaown is by far the most representative of this...some of the higher-ups, less so. Nanoha's Muggle parents are also quite understanding and helpful, for a Magical Girl's parents.
Triangle Heart 3: Sweet Songs Forever is somewhat of a partially alternate universe, but even with that caveat, Nanoha's parents (and siblings.. and shop assistants..) are about as Muggle as a desert is wet. They just don't use magic the same way, if at all.
It helps that he's at least an amateur chessmaster himself, and, being a mage in a Crazy Awesome universe, has probably seen weirder in his day.
Bradley in Fullmetal Alchemist seems to be one of these, but like Palpatine, he's really a bad guy.
Ling Yao appears to become this. To begin with he was already a Prince with the belief that the duty of a King is to serve his people and that a King is nothing without his subjects, but when he actually obtains what he needed to success to the throne, his first promise is to accept and protect each and every one of the rival clans within the Xing empire, which every generation up to then would war with each other over who will be next to inherit the throne.
Basque Grand is without a doubt one of these, doing his best to limit his men's casualties (often by leading the charge himself) and not only accepting the surrender of Ishval's head cleric (despite his own superior's orders to the contrary) but making sure that he gets to see Fuhrer Bradley, no matter what. It doesn't do a lot of good in the long-run, but given the circumstances Grand is being as reasonable as he can be.
One Piece has former Fleet Admiral Sengoku. You'd think that, being in charge of the Navy, he would be one of the most evil characters in the series - but he genuinely puts the safety of the world first. His superiors in the World Government, as well as his successor, on the other hand...
FormerAdmiral Aokiji and Vice Admiral Garp are also examples. They're harsh on pirates but will go out of their way to protect civilians. Likewise for Vice-Admiral Smoker and Captain Tashigi, Captain Coby, and even more so with the brief character Commander Ripper from the Captain Morgan arc really, despite the fact that many marines are Lawful Evil, there are some Lawful Good ones as well.
Smoker and Tashigi get to show just how much they are this trope during the Punk Hazard arc. Tashigi is even willing to beg Trafalgar Law, a pirate, to free her not for herself, but as she tell Smoker, because they cannot go help their comrades or the kidnapped children if they remain in chains. They then direct the rest of the Marines to work with the Straw Hats to evacuate the children before Caesar's gas kills them all.
We are now introduced to Prince Fukaboshi of the Neptune Army. Most people would have freaked out if they heard that their father was being held hostage inside the palace and the kidnappers started making demands (especially since said kidnappers are prophesized to destroy Fishmen Island). Fukaboshi was very calm, agreed to the demands in return of the hostages and then passed on Jimbei's message for Luffy to Zoro as part of his duty to Jimbei, whereas most people would have been "screw that" to the kidnappers.
With Aokiji's leaving his post new Admiral Fujitora has stepped into this role in a big way. Upon realizing Dressrosa is full of New World Pirates due to a tourney its ruler Doflamingo is holding he instantly...calls in medical teams for the inevitable fallout, and gets a count of how many civilians are in Dressrosa so his men know who to protect. His goal as an Admiral? Demolish the broken Warlords system that allows scum like Doflamingo to get away with atrocities. Doflamino's crew is attacking everyone on the island now? Work alongside the good pirates to keep them safe. His superiors will want to twist the truth of what happened on Dressrosa, where pirates saved the day? Fujitora gets out the information of what really went on to neighboring islands before reporting in to them so they can't change the story, fully understanding that Akainu will want his head for this.
Luffy himself. He is, after all, The Captain of the Straw Hat Pirates (as well as the Straw Hat Grand Fleet) and considered to be The Fifth Emperor. It's an understatement to say he's fiercely protective of his crew and cares for their well-being over pretty much anything else.
In Full Metal Panic? Fumoffu, the Student Council President. How reasonable is he? Well, he thinks Sōsuke's way of disposing of an unknown item in his shoelocker (i.e. detonating the entrance hall with a high-yield plastic explosive) to be perfectly reasonable. After all, anything could have been in there.
Though exactly how "reasonable" it is to automatically believe and trust in all of Sousuke'sactions is debatable, especially among the other students.
In the light novels, it turns out he's actually figured out that Sousuke is a soldier for Mithril, so that could potentially have something to do with it.
In Freezing, among all the Axe-Crazy of a Blood Knight third years, only the strongest among them, Chiffon Fairchild, is the one who isn't interested in beating Sattelizer into a messy pulp.
Both the Third Hokage, Sarutobi and the Fifth Hokage, Tsunade from Naruto, have fulfilled this role over the course of the story.
Another example is post-timeskip Gaara. Notably, he's the only one of the Five Kages apart from Tsunade, below, who pushes for cooperation between the ninja villages in response to the threat of Akatsuki.
Tsunade appears to be this because of the way she's always generous to Naruto... but that's just it, she's always generous to Naruto. She sends him up against the people who are after him, consistently allows him to go after Sasuke (as well as not actually seek to eliminate Sasuke, which would be standard procedure) and refuses to place restrictions on him that would better protect him (and the Eldritch Abomination inside him) from his enemies. She chooses to do these things entirely based on her personal feelings and opinions of Naruto, which is realistically an unreasonable thing to do. There is the fact that Naruto is The Hero of the story, is marked by a prophecy to become a Messianic Archetype, and has defeated powerful enemies that nobody else could and ruined some of the plans of the major antagonists (even if admittedly he has been in mortal peril and requiring help many times), so Tsunade's trust in him is not entirely unfounded.
The Third Hokage is later on shown to be a deconstruction or subversion; He was too reasonable. A lot of problems in Naruto's world are the result of Orochimaru and Danzo being allowed to do as they pleased, and they all could have been stopped had the Third learned to put his foot down.
In Pokémon Adventures, despite the fact that White did forcibly draft Black into her talent agency by footing the enormous bill for the movie equipment he destroyed, she doesn't actually expect him to be able to pay off the entire thing. She acknowledges that he does have his own life and dreams to follow. That said, she still tries to get him to understand the world of showbiz and business a little better, and is quick to call him out whenever he ruins a potential job opportunity.
In the undersea horror manga 6000, Wein, the director, is initially set up as a JerkassObstructive Bureaucrat who ignores his engineers' warnings that the instillation isn't ready for prime time; once he's convinced there's a real danger, though, he shows himself to be remarkably Genre Savvy, immediately arranging to evacuate the entire instillation at the first possible opportunity — going so far as to avoid informing any higher-ups until everyone is safe (because they wouldn't recognize the danger fast enough and wouldn't approve an expensive complete evacuation), declaring his intention to personally take full responsibility for any objections they have to this course of action.
The Roman Emperor from Sound of the Sky is never shown in the anime and is only mentioned as the guy Rio's older sister, Iliya refused to marry even if it would end the war. When episode twelve roles around Rio appears right before the final confrontation and claims that due to her recent marriage to him, the war is now over and during the ending credits she returns to the Bastion and tells them that the emperor is a pretty reasonable guy and granted her any one wish because she ended the war.
Captains Kyoraku and Ukitake from Bleach are this. Unlike the Head Captain Yamamoto, (who follows Central 46 orders to the letter, and embodies blind obedience to tradition above all else), these two will take the time to listen to progressive mindsets from their subordinates and non-combatants give a fair audience to the accused, and even defy tradition and law when the situation calls for it. Byakuya also becomes a variation of this after Ichigo helps him resolve an issue he had with two conflicting vows that was the reason he had been compelled to support Rukia's execution despite not wanting her to die. Captain Hitsugaya counts as well, since he realizes that something is amiss, and eventually sets out to find the Central 46 and stop the execution rather than see the Seireitei fall into chaos.
Center-sensei from His Coool Seha Girls is a fair teacher who tries to help the Sega Hard Girls whenever he can, but is not above withholding medals if he thinks the girls did not earn them (although Sega Saturn seems to get the worst of it, in this regard). For example: in the Virtua Fighter lesson, Dreamcast and Mega Drive were given no medals because they each attacked an opponent before the round actually began; then in the Space Channel 5 lesson, he awarded no medals to Sega Saturn because of complaints lodged by the Space PTA concerning her flagrant use of sex appeal to drive up ratings.
Senzaemon Nakiri from Shokugeki no Soma. As the headmaster of the prestigious cooking school where the series takes place, he is revered and dreaded as the "Gastric Godfather" and "Food Demon". However when looking at his actions it's kind of difficult to see how he got that reputation. For example, he overrode his granddaughter's rejection of the protagonist's entrance application after having a single bite of his food and realising his granddaughter rejected the protagonist out of spite, and will always give a reasoned, well-balanced critique of any food he is asked to judge. He also has a track record of not playing favorites, not hesitating to call out even members of his own family when they don't perform well enough.
Pretty much everyone in Judgment and Antiskill are this in the anime of A Certain Magical Index and A Certain Scientific Railgun. In Railgun it's not so surprising that Kuroko and Uiharu from Judgment (and by extension, their mentor) are reasonable authority figures since they're in the main cast, but Aiho and Tsuzuri from Antiskill count even for Railgun. They're not major characters, and they'll stop the characters from doing things they shouldn't be, but when push comes to shove, they'll even ignore orders from the conspiracy in order to act as The Cavalry. Antiskill in general, while often incapable of doing their job without the heroes, are savvy enough to help keep things clear for them, trusting that the middle and high schoolers will take care of things.
Taken even further in the later volumes with the British Royal Family and the current president of the United States, Roberto Katze. They both are shown to have a deep love of their respective countries, and are willing to accept the bizarre explanations Touma and the others sometimes have to give them when magical forces are at work.
Early in Ai Yori Aoshi, Aoi's mother comes to Kaoru's apartment determined to take Aoi home despite her insistence that she stay with Kaoru. However, she soon relents and even enables their Secret Relationship, provided they don't let it get out and cause a scandal. One reason for this is she notices that Aoi wanted to stay by Kaoru so much that she willfully defied her family for the first time in her life.
Kotori Minami's mother, the director of Otonokizaka High School, in Love Live!, who allows μ's to perform in the opening campus on the condition that they pass their final exams.
Digimon Adventure 02: Some militaries don't outright attack wild Digimon and observe them as long as the Digimon do nothing hostile. Special mention goes to the officer leading the Chinese army, who acknowledges that the strange creatures are intelligent and is willing to communicate with them, letting them pass through the country border, knowing that they won't cause any more trouble.
The Japanese government in Re:CREATORS treats the appearance of fictional characters in the real world in a very pragmatic way: instead of silencing everything, makes a special committee with these characters' creators working back to back with government agents, doesn't bother too much with The Masquerade since it's almost impossible to control the net and every electronic device, and instructs its agents to learn about their country's popular culture. However, the show goes almost too far in the opposite direction, since at times the people in charge seems too eager to believe in the words of several costumed whackos who know nothing of the world they found themselves in.
Despite his rather...reserved attitude towards the insanity in Yokai Academy on a day to day basis, Headmaster Mikogami really supports Tsukune and friends, is a very fair individual (though not above bending the rules if it's harmless amusement) and is a true advocate for peace between monsters and humanity. And he used magic to keep human deaths to a minimum when Fairy Tale's HQ fell onto a human city.
Ms. Nekonome is one of the few teachers who isn't a Jerkass or horribly deranged and is actually helpful and non-prejudicial to her students. When Kuyou has Tsukune scheduled for execution and Mikogami forbids her from intervening, Ms. Nekonome calls him out on it, reminding him that Yokai Academy is supposed to support human/monster co-existence.
Agent Axel Hughes in Heroman has a little fun with this. When he reveals himself to Joey and Joey asks what they would do with Heroman; he replies that they'll imprison him and experiment on him. At Joey's horrified look, he laughs and says of course not. They would want to be on good terms with him and hopefully they can peacefully learn from each other.