My point of view:
Racism is discrimination, using skin color or race as an excuse, that's the problem with it, they are basing judgement on someone else only based on one attribute, which is race. Isn't hating racist people the same?
Let them be racists, it doesn't bother me that people think in different ways, that's the whole point of having free will. Sure, now peole talk about violence acts and crap, but that is not 100% derived from racism, non-racist, non-whatever people can be guilty of the same.
It is as simple as this: people mocks you because X characteristic you have, if you get offended you are practically agreeing with them, by saying "I know x-charac is inferior, and I'm ashamed of it" If you get offended, you may need to check self-steem issues or anything.
If you don't get offended, it's only because you know that they are wrong, and are perfectly ok with yourself.