I haven't read all the replies, so maybe this is already covered. If someone accuses you of being homophobic or racist (and let's just throw sexist in there as well), the very best thing you can do in that situation is investigate their reasons for the accusations, that is, have a conversation. You might actually find that they have some valid concerns and both parties could end up learning a little something from the exchange.
I'd argue that it always helps to investigate your thoughts concerning any subject; what are they (obviously), what are the sources that help form your opinion (personal experience, articles, blogs, etc.), and can you really say you're knowledgeable enough about the subject that you've an informed opinion on the matter? Things like this will really affect the way you engage people when discussing pretty much anything.
Ultimately, you shouldn't worry too much about accusations like this unless it stands to have some negative impact on your life (eg. work), but as someone has already said, it's very hard to prove you're not homophobic (especially to someone who has made their mind up). The best thing you can do is leave them to their opinions and let time be the judge.
I'd argue that it always helps to investigate your thoughts concerning any subject; what are they (obviously), what are the sources that help form your opinion (personal experience, articles, blogs, etc.), and can you really say you're knowledgeable enough about the subject that you've an informed opinion on the matter? Things like this will really affect the way you engage people when discussing pretty much anything.
Ultimately, you shouldn't worry too much about accusations like this unless it stands to have some negative impact on your life (eg. work), but as someone has already said, it's very hard to prove you're not homophobic (especially to someone who has made their mind up). The best thing you can do is leave them to their opinions and let time be the judge.