No love for V-day.

[KodiHivaer]

Let me answer your question with another question:

Would the distinction between "black person" and "white person" still exist if we lived in a world where elves/catpeople/Martians were commonplace?

Yes, because there are Duskwights (darkskinned) and Wildwoods (lightskin), Dunesfolk and plainsfolk, Seeker of the sun and seeker of the moon, etc.
Just because it might not be the common black and white doesn't mean that there isn't a form of discrimination/stereotyping, there's still a distinction via name, skin color,class,creed and they judge each other based on clans.

Just replace black and white <someotherracehere> with the races/clans in this game and you'll get the same thing under different cultural/worldly standards/

[Almalexia]

Yes, because there are Duskwights (darkskinned) and Wildwoods (lightskin), Dunesfolk and plainsfolk, Seeker of the sun and seeker of the moon, etc.
Just because it might not be the common black and white doesn't mean that there isn't a form of discrimination/stereotyping, there's still a distinction via name, skin color,class,creed and they judge each other based on clans.

In fantasy worlds, racial discrimination as we understand it on earth typically occurs where the differences are at their greatest: not by clan or skin color, but by comparative anatomy.

As humans, we're going to align with Human sooner than Elf because we look more akin to Human than Elf. It's primitive and makes perfect evolutionary sense, but it doesn't matter what color the elf is. The nitpicky differences between sub-races melt away in the presence of another primary race.

eg. A Midlander, Highlander and Doman know they are superficially different from each other, but they are altogether more similar than a Duskwight and a Wildswood. If you put a sample of each clan into a box with limited resources, it's highly likely the Hyur clans and the Elezen clans would bond with their respective races first to secure them--before, naturally, turning on themselves.

Rarely do you see fantasy worlds with multiple intelligent races where conventional, real-world "intra-racial" discrimination exists. You still have other divisive factors like class, sex, religion, cultural practices, property disputes, magical curses and old-fashioned ignorance.

eg. in FFXIV, you're far more likely to see a Hyur--NPC or PC--call out a Lalafell on racial grounds than another Hyur, irrespective of their clan. And let's not forget the various Beastmen, who have even greater differences than the non-Beastmen races and are largely ostracized for it.