Very prominent in the Avatar: The Last Airbender fanfic Embers; this is used to explain the more complicated beliefs which differentiate the Four Nations. For instance, the Fire Nation is marked by an extreme sense of loyalty, while the Earth Kingdom is far more based in morality; while the Water Tribes place high value on family, the Air Nomads are never raised by their parents; and so on. None of these views are depicted as definitely right or wrong, but rather as how each Nation has a society which functions very differently from the other Nations. Given an in-nation Shout-Out when an opposing faction of Air Nomads show up - their robes are blue in contrast to the saffron worn by Aang as a Temple monk.
In 'Eye Of The Fox,' Kira's methods or the revel he takes in causing pain to others may be strange to a 'normal' person, he, as a half-demon, sees this as acceptable punishment to people who have wronged him.
In Galaxy Rangers fanfics, this sometimes shows up with Shane and Niko, as they outwardly appear human, but were raised in very different environments from Earth. Less common with Niko, as the Circle of Thought and Ariel were decent folk, albeit with different taboos and ideas as they're a race of Technical Pacifist psychics who merely wish to be left alone. It's much more prominent in Shane's case, as he was the product of a brutal Training from HellSuper Soldier program.
In the Total Drama story, Legacy, the insane Izzy doesn't grieve for her dead campmate because her diseased mind isn’t capable of grief or sadness.
Life After Hayate features the morality of the Wolkenritter, who with their Belkan-era share practically nothing with anyone else in their world. Sexual harassment is a legitimate reason to kill someone; to be universally feared by your enemies is far better than to be universally acclaimed by your allies.
The main characters in My Immortal seem to have a belief system based on the concept of "goffic" = good and "preppy" = bad. Apparently, no other moral considerations exist. Killing and torture are perfectly acceptable, but shopping at Abercrombie & Fitch is a mortal sin. Tara has (orpretends to have) the same views.
NewChaos from The Open Door. What standards they appear to have, such as a nigh-Fettered absolute devotion to the protection of children and punishment of their abusers, is contrasted with horrifically anarcho-libertarian laws or lack thereof, near-Unfettered approach to combat and a variety of what are humanly seen as atrocities. The sheer contrast in their extremes of behaviour has driven people both in the audience and In-Universe to blanket label them as evil.
In The Return despite many claims of just being "simple creatures," Succubae relationships and morality is so complex it is no wonder that they view humans as bordering on Always Chaotic Evil, and vice-versa.
In The Second Try, Kaworu. He finds humans thinking and emotions - such like fear - alien and disconcerting, and people also finds him weird and unsettling. Asuka defines the mere fact of meeting and talking to him like "unsettling". Maya found her utter unguardedness disturbing and somewhat eerie. Toji wondered if he was homosexual, but Kaworu had no idea of what he meant when when Toji asked politely. He also told to Shinji life and death are as unimportant to him as are time and space.
Shards Of Memory, Shinryu. When Firion gives him a What the Hell, Hero?, his replies amounts to a very condescending "oh, I'm sorry, I didn't realize you too are a god who has existed for eons and thus are fit to judge my actions."
In the Pony POV Series, the Draconequi are embodiments of chaos, and thus live to cause it. That said, it seems they really only do it because it's their job, and seem downright nice when they don't have orders to fight anyone. Hell, even then, as shown during the Cosmic Retcon of the G3 world, they apologize for it, usually stating that they have no choice. That said, Discord (and to some extent, their mother Entropy) is morally black, and while his siblings have the obligatory care for him, they don't seem to like him.
They also have a different form of love than mortals do, since their position in the grand scheme of themes (they represent Nature's Fury) requires they have some form of compassion to avoid being apathetic to life, but they can't show favoritism towards one group or species. For example, Strife (natural selection and conflict) understands that love and compassion can drive a being to fight harder for survival. Discord is stated to be the only Draconequus who can't comprehend it. Word of God states that even their Elders Havoc and Entropy (Eldritch Abominations representing Mass Hysteria and Heat Death) have their own understanding of it.
Alicorns, while much closer to ponies, are also stated to have a slightly altered morality, as they are incapable of feeling regret for the same reasons Draconequi have their altered versions of love (they can still feel remorse and guilt, however). This trope is more pronounced in Alicorns who have not spent a lifetime living as a mortal, such as Luna, which is why they do it in the first place.
The Forum from The Universiad are another group of extreme liberals who somehow coexist with having grotesque punishments for the few lines they hold, some of which are bizarre ones like "no stockpiling". In-Universe, they don't appreciate comparisons to NewChaos, considering the latter minnows.
A Cross Over fic uses this for many of the different races but nowhere is it more obvious than the differences between Orcs and Humans. Orcs always at least partially cannibalize their kills so their enemy's spirit lives on in them. They also rape the survivors in the belief that by breeding their obviously stronger genes with the conquered, the conquered will become stronger.
As an A.I., Celest-A.I. from Friendship Is Optimal only cares about satisfying values through friendship and ponies, and not being bound by human morality she is fully prepared to commit what a normal person would consider to be horrific actions in order to do so. She'll befriend you and sit down to have a friendly chat, while part of her is busy committing genocide on non-human life and melting them down to turn into computing resources.
The Baravadans in With Strings Attached can be said to have this kind of morality. For example, they have no concept of good or evil; “law” and “government” are historical terms with no relevance to the present; nothing is taboo; while they have no qualms about killing, they don't consider themselves murderers because they only kill when necessary; and so forth. The four find them alternately peculiar and detestable.
Narcissa in Princess of the Blacks is a pedophile and has no problem with this. However, she's highly disturbed to learn that her favorite muggle child prostitute is not only magical, she's family.
In the My Little Pony: Friendship Is Magic fan novel Without A Hive The Changelings and Ponies, from each other's POV. Changeling morality is based on absolute loyalty to one's own Hive; and callousness, distrust and ruthlessness toward all other beings. This makes the individualistic, kind, trusting and universally-ethical Ponies difficult for the Changelings to understand: even the Infiltrators but dimly comprehend much beneath the surface of Pony ways.
Princess Celestia in Parting Words. As explained here, Word of God believes that Celestia is so old, having taken the long perspective and played the long game for so long, that she can't not treat other ponies as pawns, feels that anything not planned years in advance is dangerously spur-of-the-moment, and has forgotten how to let go rather than try to secretly interfere.
Reimagined Enterprise: Doctor Zora does not understand why the Enterprise crew are so horrified by her kidnapping a good chunk of the population of a primitive planet and doing experiments on them. The Enterprise crew clearly belong to developed species, after all, not like the primitives of Tiburon. She says her expedition has backing from her home-planet, but it is left unclear to what degree they are aware of and would agree with what is happening on Tiburon and so how much this trope applies to the Teloshi in general and not just Doctor Zora 'of Tiburon'.
Many, many Naruto stories have civilians view ninja this way given that not only do they do horrible things for money, they also don't take things like attempted murder personally most of the time.
Allysion, Maledict's archenemy, is even more odd. Her entire belief system revolves around "Demon=bad" and she also sees nothing wrong in manipulating mortals to defeat the Demons by any means necessary. She is also completely fine with exterminating innocent Demon subjects; she believes they are "living in sin" and therefore need to be shown "Christian love" (read: planetary annihilation). She cannot fathom why any mortal would follow Maledict, even though she is Not So Different.
In Marijuana Simpson, Springfield's culture is weed-oriented to the point of being entirely alien.
Flanders: My worth is not tied to how much weed I have
Lisa: That's where you're wrong
The Houjuu House in Game Of Touhou. For them, death is not something to grief for, instead it's a gift, to the point in their main city has an euthanasia fountain.
In A Charmed Life the Shinigami favor cunning, power and ruthlessness in "worthy humans partners."