>>2 is right. That's silly.
I'm sure you probably realize this but you didn't actually do anything wrong. This person is being delusional and your acts of friendship misconstrued for some sort of advance, which, to an extent, one may control, but in this case it's in her head and you can't really do any spring cleaning in there. Sexist and homophobic for being straight? That's ridiculous. Saying you're homophobic for being straight would be like saying somebody's an animal hater for not owning a pet, or racist for not being a race they're not; that simply makes no sense and it sounds almost like that she's attacking you and lashing out to cover up embarrassment or something like that. I'm not entirely sure what you should do, since I haven't been in a situation like that, but I'd probably try to talk to her about it; if she actually cares about you she'd hear you out and you could continue being friends, otherwise, be honest with her and yourself and stop hanging around her if there's no other way to deal with it. As for the rumors, don't pay any heed to them; treat everybody like you usually would, politely and nicely and with consideration, you know, and they'll be able to see for themselves that the rumors have no merit. If they can't see them, that's another problem entirely for them to deal with as people.
In any case, I wish you luck and hope that this blows over smoothly. If it doesn't, I hope the detachment isn't too bumpy.