In any discussion of prejudice and discrimination that you haven't personally experienced, it's really just best to sit back and listen.
Too many people use their own (and often very different) experiences of discrimination as a defense against the possibility that they may not be entirely free of the prejudice being discussed. 'Cuz, you know, none of us really are free of prejudice, what's important is whether we let it rule our lives.
Too many people use their own (and often very different) experiences of discrimination to make the discussion about themselves and escalate in an Olympics of suffering and oppression. After all, it's only the most oppressed who should really have a say, right? Didn't think so...
Sit back and listen. Use your experiences of discrimination to cultivate empathy. Let the discussion be about what it's about. Offer support. Attempt to ask intelligent questions. Let the people who feel aggrieved work through things, and take advantage of the learning experience presented. Examine the differences in their experiences of prejudice and discrimination. Evaluate the extent to which your thoughts and actions feed into further prejudice and discrimination.
Then, when a discussion about your experience of discrimination and prejudice starts (and yes, that includes "when you start it"), and somebody comes along and attempts to derail it with stories of their own oppression, you can say "Hold it. I listened to your experiences. I examined my own prejudice and discrimination, and try to use what I learned from you to act in a better fashion. Please do me the same courtesy."
Oh, and read "Mary Anne Mohanraj Gets You Up to Speed, Part I" and "Mary Anne Mohanraj Gets You Up to Speed, Part II" at John Scalzi's Whatever if you want an interesting take on the subject of racism and F&SF.