That's close to my opinion. I figure that as long as people like heintzer (above) are around, claiming that all whites are racist against everyone, and it's impossible to be racist against a white, there will be racism. But I completely ignore race. I have black friends, white friends, asian friends, australian friends (and, though it isn't under "race", I felt I'd point out I also have friends in wheelchairs)... No British friends (at least, not that I know personally), because the one British person I've met was an irritable A$$hole. Doesn't have to do with their race, just that I hated them as a person.
I judge people as people. If you're a dick, you're a dick, and I don't care about your opinion regardless.
I'll admit, I may be subtly racist in that I try to avoid the issue of race when I'm around anyone of a different race, but because that's a rare enough subject as it is, I'm normally fine. Though, you cannot (actually, you probably can) imagine how uncomfortable it was to go through the "Civil Rights Movement" (including the rise of the KKK) with someone who was black sitting right next to me in class. It did give me an interesting perspective on it, though, because I wondered how they saw this, when it was a group they belonged to being persecuted. (P.S.: They didn't care. They basically paid as much attention as you could expect anyone else their age to.)