I have to say that I don't really find the stereotypes to be true. I know HUNDREDS of queer people - mostly gay men - but also lesbians, bisexuals, transgender, etc. and, in regards to gay men - let's see, I've met the queens, the hairdressers, the art fags (my personal fav and stereotype that I fall into, I suppose), the gay jocks, the club kids, the fashionistas and the socialites, the theater gays, ravers, bears, blah blah blah. There's a ton of different kind of gay people. Is it possible that there are, in terms of an overall demographic, more artsy types in the gay community that overall? Maybe. But when I think of all the gay artists I know, then I just think of all the queens I know, who aren't artists at all. I would say the biggest stereotype that I've seen, in reality, is the bimbo-homo obsessed with pop culture, fashion, celebrities, and generally boring shit. Like the stereotype of a "dumb chick". But then I've met lots of alternative hipster gay boys too.
I would have to say the tendency to stay away from sports has to do with, like the other poster said, withdrawing from the group of men during puberty because of your confusion, etc.
That line of thinking would also explain a tendency for the arts. Who are artists? People who express themselves through a certain medium, often things they can't easily express. It makes sense that gay people would be turned on to things like writing and the arts.
Plus, we're just more creative and brilliant in general.