An American Tail is an obvious one, the mice represent the oppressed ethnicities of the world and the cats represent their oppressors.
A major focus of the The Animatrix was the growing distrust between humans and robots, growing out of humans treating robots as inferior slaves; ultimately this led to a robot purge, followed by the surviving robots leading a successful rebellion. The historicals parallels are plentiful.
It's also to show how in fighting against blatant specism, the robots themselves became what they fought against. In the end, the oracle from The Matrix didn't want humans to have revenge on all machines, but to end the senseless, endless war between humans amd machines, to have peace and love...though it helps that the oracle herself is part of the machines; a piece of code that has seen the rise and fall of humanity, several versions of Zion, and several "The One"s...
Bluebeard in the animated film Felidae refers to humans as "Can Openers" believing that the only thing a human is good for is opening cans of food for cats to eat. Yes, a cat making racist remarks about a human.
Claudandus takes this even further believing that humans are pure evil. To be fair, he was subjected to horrific experiments by a human until he killed said human.
'Claudandus: No, no! There are no good humans! They're all bad! Animals are good creatures. But, humans? Humans are evil'' animals.
He's also racist against other breeds of cats, since he murdered any cat he deemed "unworthy" of mating with his "superior" breed of cat he had created through selective breeding. This should come as no surprise, since the film (and the book it's based off of) draw parallels to Nazi Germany.
In Frozen, the Duke of Weselton Does Not Like Magic and reacts with incredible fear and hatred to witnessing Queen Elsa's ice powers, quickly convincing his men that she is a monster who must be destroyed. He also takes time to harass Elsa's normal sister Anna, asking if she's a monster as well.
Even if they did so for good reason, Manny and Sid were wary of Diego in Ice Age at first mostly because he was just a saber-toothed tiger.
The first The Land Before Time movie contains plenty of Fantastic Racism between the different species of dinosaurs. The "races," stay in their own groups at the movie's start, these being the Long Necks, the Three Horns, the Swimmers, the Fliers, and the Spike Tails just to name those of the main Five-Man Band. Most, if not all, of the Fantastic Racism is gone by the movie's end, when all of the dinosaurs, sans Sharptooth, are living in the Great Valley in peace.
This shows up in the sequels as well. In every single one, Cera's (the threehorn) father forgets the 'racism is bad' Aesop and tries to blame the new problem on anyone and everyone else. The plot unfolds, and by the end he repents for being such a jerk...until the next time. There is also a saccharine song called "It Takes All Sorts" on the subject.
Lord Farquad of Shrek is aptly named. He hates all "fairy tale creatures" and his self-proclaimed "perfect world" is one where they have all been removed. From what we see in the film, his kingdom is undergoing a family-friendly form of genocide against any and all living things that are magical or supernatural in nature, including human wizards and witches, leaving only Muggles behind. Oh, and he's a complete hypocrite since he's a dwarf (and not a human with Dwarfism, an actual dwarf).
Toy Story 2: With the launch of Sputnik and the Space Race in the 1960's, children became obsessed with toys related to space and all other toys fell into steep decline quickly. This isn't true in modern times, but the old cowboys-themed toy Stinky Pete hasn't quite got over this old grudge, and in his own words, "space toys" like Buzz are upstarts.
In Wreck-It Ralph, the video game villains are treated so poorly that they need to create a support group, while the characters of Sugar Rush act this way towards any and all glitches (though it is possible this is wholly due to King Candy reprogramming Sugar Rush).
Eduardo in Rio 2 is harshly opposed to anything and everything to do with humans; he orders his flock to stay out of their sight, and criticizes Blu for using human artifacts.
Films — Live-Action
Matt Sykes of Alien Nation has a black partner (they're cops) at the beginning of the story but refers to the alien Newcomers as "slags" before he's been told that his new partner will be a Newcomer. Of course, by the end Matt has been converted.
James Cameron's Avatar is a perfect example of this. The interactions between the alien Na'vi and the humans parrallels indigenous cultures meeting Western explorers and colonists. Most humans see the Na'vi as primitive savages to be exploited for their land's natural resources, while a few scientists genuinely want to communicate with and study them. The Na'vi are distrustful toward the humans, whom they see as greedy invaders and culturally inferior barbarians.
In Blade, pureblood vampires treat people who have been turned into vampires with disdain.
This forms some of the plot of both the original film and the TV series. Both Frost and Van Sciver are turned-bloods and are forced to bow down before the purebloods. At least Frost is open about his disdain for them, thinking that they're stuck in the old ways, ignoring the modern world. Van Sciver always shows them reverence, while cursing them behind closed doors. With Van Sciver, at least, a plausible explanation for this is the death of his wife and his forcible turning at the hands of a pureblood.
In Blade Runner, we have humans using 'replicants', who are seen as Just a Machine. The racism aspect comes in when one of the characters refers to replicants as 'skin-jobs'. In one of the editions, a lampshade is hung on this, with the protagonist comparing him to the type of cop who used to call a black person a nigger.
In District 9, aliens who arrive on Earth are treated as second-class citizens and forced into ghettos by the South African government. Parallels to apartheid are obvious, but the writer insists that it's not an allegory for apartheid. The film deals as much with hostility of black Africans toward the aliens as the white members of government. The director coaxed Enforced Method Acting performances from local South Africans by asking them what they thought of immigrants to use as "man on the street" criticisms of the aliens. The original short film, "Alive in Joburg," however, does specifically mention that the government used apartheid laws against the aliens.
In Gattaca, Designer Babies are so common that any one born through "old fashioned" means is thought to be inferior and can never get any decent job. The Protagonist himself one of the outcast points out that discrimination is brought down to a science.
Played for laughs in Jim Henson's Hey, Cinderella!. For some unspecified reason, no one but Cinderella and the prince are willing to listen to frogs. This means that poor Kermit spends the entire movie trying to clear up the misunderstandings, only to be ignored. The king also makes frogs the only exception to his proclamation that everyone in the kingdom is invited to the ball, and we later see that frogs aren't allowed to give testimony. We're also told that Cinderella's dog Rufus is unable to testify that she's telling the truth, but that might be justified as a dog being biased in favor of its owner.
In The Hobbit, there were hints that there was racism towards the dwarves mirroring real-life antisemitism and hostility towards the Gypsies. Even Bilbo insensitively snapped a comment about the dwarves "not belonging anywhere" though he quickly apologized and was ashamed of it afterwards. Also, Thorin openly dislikes elves and despises anything that is elvish due to his previous experience with them.
In I, Robot, Spooner hates robots. His hatred of them stems from an experience, a car accident that sent him and another car into a freezing river, and a little girl was trapped in the other car. A passing robot calculated that it only had time to save one of them and that Spooner had a higher chance of surviving, so it saved him instead of the girl. In real life, rescue workers and medics are expected to make such decisions regarding who gets care first, it's called Triage. However, Spooner argues that a human would have understood that regardless of the girl's low survival chance, the life of a small child should take priority over the life of an adult.
The soviet socio-political satire film Kin-Dza-Dza features this based entirely on whether a device pointed at someone shows a green light or an orange light, dividing them between "patsaks" and "chatlanians", the planet that most of the movie is set on is owned by the chatlanians and so the patsaks need to wear a bell clipped to their nose, squat in front of anyone who is higher than them in society and perform in cages. Add this to the fact that they have absolutely no rights and you have the basis for a near perfect example of this trope.
It also should be noted that, unlike many other examples on this page, patsaks weren't portrayed as being any better then chatlanians. On planets that belong to patsaks chatlanians have it exactly as bad as patsaks do on theirs.
The Bug clearly despises humans, and refers to them by a variety of unflattering terms, including "undeveloped pond-scum," "monkey-boys," "meat-sacks" and "milk-suckers." The rest of his species, according to K, are probably very much the same.
This seems to be a major factor of most aliens as K explains that human thought is so primitive it's considered an infectious disease in the better galaxies.
Agent J uses this to provoke the Space Cockroach into attacking him by crushing normal cockroaches under his feet.
While never stated outright, The Muppets seem to be social minorities and outcasts in many of their movies in contrast to the usually successful and exclusive human societies.
Of course, this could just be because their variety show, while entertaining to us, is considered inept within their fictional universe. And even with that, popular human celebrities were (almost) always thrilled to be appearing on their show, and rarely seemed to notice that the Muppets were not human.
Also the way that Blackbeard (and judging by the number of skeletons, numerous others that have gone questing after the Fountain) treat the mermaids. They even refer to her as "the creature" and revel in how cruel and torturous her suffering and death will be.
Although to be fair there were legitimate reasons to regard the creature this way, as the mermaids were highly predatory (essentially sharks) and she eventually killed even the man who rescued her simply because it was in her nature to do so (although the last bit is still debated).
In Pleasantville, when people and places start turning color, a backlash movement starts to keep Pleasantville "pleasant" and Deliberately Monochrome. This involves hanging signs saying "NO COLOREDS" and starting anti-color riots. It even features a courtroom scene that references the one in To Kill a Mockingbird, with the residents of color segregated to the balconies.
In Predators, its revealed that the "Classic" Predators are hunted by the larger, more aggressive newer Predators. One of the classic Predators is kept chained up as a prisoner in the Predator camp, and combats the leader of the new Predators when released, but is killed.
A very low key one in Sky High but those on "Hero Support" are often looked down upon by those deemed hero worthy. Said the least it becomes a plot point later on.
In Starship Troopers, a TV presenter says he finds the very idea of intelligent Bugs offensive. This undercurrent is also hinted at after a soldier continues to angrily shoot an already dead Bug, covering himself with alien gore.
Soldier: Ain't much to look at after you scrape them off your boot.
Droids, while apparently sentient, are clearly treated like second-class citizens at best and chattel slaves at worst. At the end of A New Hope, C-3P0 and R2-D2 are clearly shown excluded from the awards ceremony. Also, the barman at the Catina hates droids. While some people have pointed out that droids would just take up space in a dining establishment, the barman clearly states, "We don't serve their kind here," and "We don't want them," suggesting that he was deliberately withholding some sort of potential service.
It is explained in the EU that the Empire would use droids to spy on the bar patrons, making it impossible to carry out their dealings; hence the ban on droids.
It may also be because of the Clone Wars.
The Empire is practically this incarnate and also has Fantastic Chauvinism. They not only hate non-humans, but specifically developed a virus to kill them in the most graphic, painful, and brutal way possible. They even have their own policy focused around racism, NhM, or Non-huMan. Grand Admiral Thrawn, one of the galaxy's best tacticians, was only accepted into the Imperial military's ranks by the Emperor himself, and that was only because of his tactical genius.
Played with in Thor. While there is no little amount of bad blood between Asgardians and Frost Giants, Odin adopts Loki, a Frost Giant by birth, raises him as one of his own, and has no prejudice against him. Oddly enough, Loki thinks that destroying the entire Jotun race would please his adoptive father.
Thor's attitude towards the Frost Giants at first and Loki's comment below hint that racism and unacceptance are still present in Asgard.
Odin: I wanted only to protect you from the truth. Loki: What, because I... I... I'm the monster parents tell their children about at night?
In the Michael Bay's Transformers: Revenge of The Fallen, the Fallen's only apparent reason for wanting to destroy Earth and starting the war that destroyed his homeworld was a general and strong hatred for humanity. Considering on his first encounter they were as dangerous to him as ants are to humans, one can only wonder.
Some humans give as good as they get and treat Transformers as just machines even though they are really Mechanical Lifeforms. This is one of the reasons Sentinel Prime hates humanity and is working alongside the Decepticons to enslave them. As a Prime he was a living god on Cybertron. On Earth, he's treated with as much respect as a toaster.
In Underworld and Underworld: Rise of the Lycans, the two races of immortals, vampire and werewolf spend entire centuries killing each other over a grudge. The vampires are more typically racist, calling the Lycans (werewolves) animals and vermin and generally hunting them to the brink of extinction. In the feudal era, the vampires kept the Lycans as slaves and pets to guard them during daylight hours. The lead vampire killed his own daughter because she fell in love with a werewolf and carried his child.
Although for several generations up to and including that one with the sole exception of Lucien werewolves WERE just animals...animals that needed to be hunted and controlled to prevent their indiscriminately wiping out the vampire's food supply and human peasants in general
In Who Framed Roger Rabbit, toons aren't allowed in certain clubs (despite being the main performers), Eddie has a slight dislike for toons after one killed his brother, and when Roger is accused of murder, he potentially faces execution without any chance of a fair trial. Judge Doom also outright murders a toon shoe that had literally committed no crime at all, and gets away scot-free.
Oh, and did I mention that Doom has plans to wipe out all of Toontown, where these toons live, and replace it with a freeway? And the plans are being concocted by someone who is actually a toon himself? Fantastic Racism, indeed!
In Willow, the Daikini (humans) call the Neldwyn (Hobbits with the serial numbers filed off) "pecks" in a clearly offensive way. Even Madmartigan, who later becomes Willow's friend, calls him this when they first meet. "Daikini" itself seems to be a mildly offensive term.
Done in the at least one version of The Wind in the Willows. At Toad's trial, the judge gives him an extra twelve months' imprisonment for being green.