Unfortunately, many race based slurs that would fit EVE races would also likely be offensive OOC too, even if we made them up from scratch. Like, anti-Brutor comments, or anti-JinMei comments.
In our unfortunate reality, race based slurs are always themed around the difference between the one issuing the slur, and their observation of the target. Thus, to a fat white Republican redneck, blacks are "niggers" because of that whole "niger, neger, it means black in french LOL ur skin is darker than mine" thing they so adorably cling to; Asians are "chinks" or "slants" because their last name might be Chang, or because their eyes are slanted.
So, what would an Amarr racist observe about the Minmatar? He can't just call them niggers, because most of them aren't black. But they are all tribal, and their spirituality differs vastly from that Amarr racist's. So let's run with that instead. "Wretched inbred savages," that Amarr would say. "Faithless, godless reprobates." "Flea-bitten cattle."
What would a Caldari observe in a Gallentean that disgusts him? "Self-centered perversion-monger." "Entitled meddler." "Egomaniac."
What would a Gallente who hates Caldari observe? "Statist authoritarian scum. Do you have a single thought in your head that wasn't issued by your parent corporation, you drone?"
What would a Minmatar who hates Amarr observe? "Wrinkled old wretch bowing to a false god that gives you permission to conduct any atrocity."
Etc etc etc. Remember. When a racist insults another race that is not his own... he will always list the things that race is worse at, than his own. This is because the racist is insecure. The racist has been brought up believing that he is superior... but as he encounters more and more evidence that his beliefs are not only wrong, but offensive to civilized people around him... he grows hateful. More desperate to reinforce the perceived dominance of his race, his people, his group. And he invariably does this by pointing out what's wrong with the other group.
I would suggest that we not rely on any racist traditions from modern day, but invent new ones.
And here's the kicker. They have to make sense. Because even in the real world, they do. That fat white Republican redneck? He tosses around terms like "nigger" because he is, in fact, and undeniably...
terrified of black people. Any slurs you come up with for New Eden's diverse populace to employ, have to be rooted in this. Racism is not just hate. It is also fear. It is in fact, mostly fear.