I've been playing pen-and-paper RPGs for more than twenty years - I'm quite happy playing anything at this point. (Unless they're voiced in the game with a very annoying voice, like two of the three male voices in Saints Row 2 - I just set it to the Jason Statham ripoff and get on with playing.)
What does put me off, though, is when I'm asked to be attracted to utterly unsympathetic characters (Kaidan, for instance), or "fall in love" with a male character (Kaidan, again). I don't mind playing a character attracted to males, but (being very straight) it doesn't resonate with me or create any immersion into the romantic subplot.
In KOTOR, for instance, I romance Bastila every time I play as male!Revan (could have something to do with Jennifer Hale's voice acting), but in at least three play-throughs as female!Revan I've never yet romanced Carth.
Similarly, in lots of playthroughs of Mass Effect and ME2, I've pursued (as male!Shep) romances with Liara, Ashley, Kelly, Miranda and Tali (not creepy bald girl, though). As female!Shep, though, although I've played a couple of the male-romance subplots, I just can't feel connected to them, so I generally don't bother. That said, it's hard not to enjoy a spot of female!Shep/Liara... (My wife's bi. I'm allowed.)