If you think that anyone can be guilty of making a racist comment or performing a racist act, including you, and that you are willing to take ownership of your statements and actions, resist blaming the person who was offended, figure out why they were taken as racist, apologize, and not do it again, post this exact sentence in your journal.
As I need to rephrase it about myself:
I'm a racist. I have white skin in a society that privileges white skin. I have enough money to consider myself middle-class, in a society that privileges money. I am reasonably able-bodied, in a society that privileges able-bodiedness. I had parents who encouraged me to do well in school, in a society that privileges education. I am cisgendered and heterosexual, in a society that privileges conformity. I have privilege, which equals power, and I have grown up in a society steeped in racial prejudice, and so I am prejudiced. Prejudice + Power = Racism, ergo, I am a racist.
But I try not to behave like one. I try to be egalitarian. I sometimes succeed. And when I don't, I hope that my friends will kick my ass as hard as necessary for me to get the point that once again, I fucked up. And when that happens, I will do my damnedest to accept that I fucked up, to apologize, and to not do that same thing again. Ideally, the next time I fuck up, it will at least be different.
ETA: One of my newer LJ acquaintances, popfiend, has asked that people who post the sentence above also link to this post in his journal. Part of the post and some of the comments are about the distinction between "what you just did" and "what you are". The argument is made, validly in my opinion, that one can do something wrong without being that wrongness incarnate (specifically, one can say something racist without necessarily being a racist).
I also think the converse is true, and that's the point I'm making above: I can't escape having grown up in a society filled with systemic racism and I can't escape my own privilege, but I can still try to act like a decent human being.
ETA some more: It occurs to me that I should mention also that I'm female in a society that still tends to privilege male; I grew up Jewish and now consider myself Pagan in a society that still tends to privilege Christian; I'm fat in a society that privileges thin; and I'm openly kinky in a society that has its head up its ass about sexuality. Those aspects don't "counteract" or "balance out" all the privilege I do have, but they may help to give me some slight insight into what it might be like to be on the receiving end of an "ism".