I have no problem with homosexual characters whatsoever. They're often very fun individuals to be around, much like those we encounter in real-life. In society in general, I think homosexuals are very important for many reasons, but I'm not going to list them here in fear of starting a political debate xD.
I can't say I have any homosexual characters in my character stash. Mainly because as a heterosexual person, making something homosexual isn't an idea that crops up immediently in my mind out of instinct or habit. I'm not saying straight people can't or don't make gay/lesbian/bi characters because that is not true. That is just how it is in my mind.
Sometimes I ask myself a question, (especially since I have a tendency to make realistic characters): "Can animals be homosexual?" Since we don't know for sure what makes humans homosexual, it's hard to say whether animals can be too. Although, we had a cat once, called Marvin, that we were convinced was gay, and our other cat was homophobic and that's why our other cat hated him XD. But in all seriousness, I see potential for an interesting piece of research there.
I wouldn't mind if a same sex character decided to crush on my character though. Since this is a game, it doesn't really matter who's crushing on you or not. And unlike the close-minded minority of individuals, I appreciate the fact that everyone has different sexual preferences.