I'd also add 'sexist' up there with racist and homophobic.
If it's my dad, I typically let it slide because I've argued with him before and I can't change his mind. I also sometimes don't speak up because I don't want to be that person who argues about everything and has to enforce her views as being the only acceptable truth. (Which I just did in #asr on a grammar/spelling issue.)
It mostly depends on how safe I feel in the company I'm in. Among my good friends, I feel comfortable enough to speak up when something strikes me as wrong. It rarely happens that I need to. But generally I'm a bit coward and worry about what people will think of me.
I'm only slightly more likely to speak up about something that offends me personally, and much more likely to speak up against something that could offend someone I care about. Afraid of being seen as oversensitive, I guess.
Oh, and it REALLY bothers me when someone says "no offense" - the term is "no offense intended" - just saying "no offense" strikes me as "you are not allowed to be offended by this because I say so" instead of "I don't mean to offend"