"Fantastic" as in "fantasy" or fictional, not as in "awesome", obviously.
Now that we got that out of the way, Fantastic Racism is a subset of the old trick of dealing with thorny issues through metaphor. Instead of having The Hero encounter racism between, say, white and black people in the American Deep South, or between ethnic Czech and Roma in the Czech Republic, or between Ainu and Japanese, or any other sets of real-world groups, they encounter "racism" between two-headed aliens and three-headed aliens, or between people with earth-themed elemental powers and people with water-themed elemental powers, or between shapeshifting squid-people and shapeshifting octopus-people.
Not to be confused with Space Jews, in which an imaginary species or culture has disturbing similarities to a real-world racist stereotype. Also related to Have You Tried Not Being a Monster?, where said monsters are usually used as a metaphor for other types of discrimination, oftentimes discrimination based on characteristics perceived by the bigot to be alterable, "curable", such as an alternative sexual identity, a disability, or a different religion/religious differences (the two tropes can often overlap in the case of religion), rather than race or ethnicity. Fantastic Slurs are often involved, as are Monster Rights Movements. Real Life weaselly lines like Some of My Best Friends Are X may feature. The undesired minorities may be rounded up inside a Fantastic Ghetto, and may also be the targets of Superhuman Trafficking. Conversely, they may form an Outcast Refuge away from the oppressors to live in (relative) peace.
Futuristic science fiction examples of human-on-alien Fantastic Racism will often make the human racist a member of a group historically discriminated against on Earth (such as a black character in an American-created work) both to emphasize that human-on-human racism is a thing of the past, and for the sake of irony from the viewers' perspective.note
If the point of the story is to show the evils of racism, this trope can lead to a Broken Aesop if there are in fact good in-universe reasons to discriminate against a certain type of creature (say, because they need to eat other sapient beings in order to survive, or they genuinely are Always Chaotic Evil apart from the odd angsty heroic one, or they're just potentially-dangerous enough that one doesn't strictly have to be an absolute incorrigible raving xenophobic lunatic to consider making certain... precautions (at least against the loose cannons) to be a good idea).
Also note that Tropes Are Tools: most people wouldn't believe in a world where elves, dwarves, aliens, etc got along with perfect harmony, because their own experiences of different groups' interactions don't bear that out. It's called Fantastic Racism for a reason.
If the racism appears to be spilling into something a little less fantastic and into something more real, it's Values Dissonance.
Compare Superior Species, in which one species actually is objectively superior in some way; Species Loyalty, which may but does not need to entail this; and Master Race, when it's just in their head (and is probably a metaphor for Those Wacky Nazis for further bad-guy points).
See also People of Hair Color (which can be another occasion for racism in fantasy), Dehumanization (where one race is dehumanized to make them easier to kill) and Demonization (where negative character traits are fabricated, exaggerated, and generalized in order to justify some form of prejudice and hatred). Death Means Humanity is one potential resolution to any conflicts born from fantastic racism in which the death of a non-human being makes a human character recognize that being's personhood and value.
- Androids Are People, Too: Human-like robots want to be treated equally to actual humans.
- Animal Jingoism: Conflict between any two kinds of talking animals
- Anti-Human Alliance: When non-humans (or transhumans) declare war against all (normal) humans.
- Call a Human a "Meatbag": When humans or other fleshy, organic beings are called 'meatbags', 'fleshbags', or other evocative terms by less meaty beings.
- Cat/Dog Dichotomy: Felines versus canines.
- Clash of Evolutionary Levels: Conflict between a species and their evolutionary successors.
- Clones Are People, Too: Despite what some say ins-universe, clones are actually just as real and human as natural-born people, and wish to have the same rights as they do.
- Dogs Hate Squirrels: Self-explanatory.
- Elves Versus Dwarves: Elves versus dwarves.
- Expendable Clone: Cloned beings are treated as mass-produced, cheap copies and easily-replaceable objects, that aren't even granted the dignity of being considered as "real" people.
- Fantastic Ableism: People with Fictional Disabilities are mocked by what the setting considers an able-bodied person.
- Fantastic Ghetto: De jure or de facto urban segregation against undesirable races or species.
- Fantastic Slurs: Species-specific insults and profanity.
- Fantastic Terrorists: Extremist militants whose goals and ideology are in some way motivated by conflict and prejudice between fantasy races.
- Fantastic Underclass: The lowest level of a fictional social hierarchy, consisting of races or species who are despised and oppressed by their social superiors.
- Fur Against Fang: Werewolves (or other animalistic shapeshifters) versus vampires.
- Half-Breed Angst: When a hybrid person feels severe insecurity over not fully belonging to either side of their mixed heritage.
- Half-Breed Discrimination: A hybrid character is discriminated against by one or both of their parents' species.
- Have You Tried Not Being a Monster?: A different kind of metaphor, somewhat more like Fantastic Homophobia.
- Inhumanable Alien Rights: By definition, non-humans cannot be protected by the laws of human rights.
- Just a Machine: Humans versus robots and artificial intelligence.
- Kill All Humans: The (attempted) genocide of Homo sapiens sapiens.
- Maligned Mixed Marriage: When bigots direct their ire against the parents of a hybrid for daring to cross the sexual and genetic boundaries of their respective species.
- Muggle Power: Normal humans hating people who use magic or superpowers.
- Pets Versus Strays: Domesticated animals that live with humans versus feral animals that live in the wild.
- The Right of a Superior Species: A more advanced species believe they have the right to bully and subjugate a more primitive species.
- Robots Enslaving Robots: One type of robot oppresses another type of robot.
- Son of an Ape: When humans are derided for being primates by nonhuman beings.
- Superhuman Trafficking: Kidnapping and enslavement of special people to exploit their superpowers.
- Super Supremacist: Superhumans despising normal people and believing they should rule over them.
- Unequal Rites: Rivalry between different types of magic users.
- Van Helsing Hate Crimes: When a monster hunter indiscriminately attacks innocent monsters only for being monsters.
- What Measure Is a Non-Human?: Humans versus all other species of (sapient) beings.
- Xenophobic Herbivore: Not all herbivores are friendly. Many of them are (understandably) afraid of predatory animals.
- Zombie Advocate: Civil rights activists working for the equality of unusual minorities; sort of an inversion of Fantastic Racism.
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