Racism doesn't need to involve blathering idiots who want to burn your house down, all it takes is someone to treat another person worse because of their race.
Which is to say, we're all at least a little bit racist. One of the greatest lies of modern society is that racism is somehow exceptional, or intrinsic to a character, when it is in fact highly contextual and can be brought out of anyone.
Race in dating is very heavily influenced by popular perceptions of particular races, including stereotypes - that someone won't give a black person the time of day even if they are articulate and hit other criteria is racist, though the fault here seems to lie more with society than the individual.