So your friend felt it necessary to tell all her new friends about her gay best friend back home... and then her new friends made up a completely erroneous mental image of you. That's their fault, not hers. Nevertheless, I think it behooves you as her friend to talk to her about this. You don't have to be confrontational about it, just ask her why she refers to you that way.
My best friend used to go around referring to me as "my gay best friend" until I confronted her about it. Why am I your gay best friend? Do you have another best friend from whom I have to be differentiated? Do you suppose I refer to you as my "female best friend"?
She was rather surprised by the comparison: she'd never thought about why she referred to me that way. Probably to underline the fact that we're friends, we're not dating, and so she is completely available. Also to warn people that she's not going to take any shit about gaybashing and homophobia from them.
I assume your friend is very young; one of the worst common failings of the very young is to insist upon explaining themselves all the time, a habit of loading their conversations with all manner of useless exposition. Maybe she thought having a gay friend made her seem more hip, maybe it made her seem more progressive, maybe it made her seem more available to men... I don't know. And neither will you know unless you talk to her about it.
But in general, this is one of the things that happens when you're a minority of any kind: you get lionized for it when you hang out with people who are not of the same minority. Unless you are completely surrounded by your own kind (which is very limiting) or by the fully socially evolved (which is impossible), you are going to be somebody's gay friend, somebody's black friend, somebody's atheist friend. It happens. You deal with it.