Peter Parker is an underdog because he was smaller, weaker, and more timid then his classmates. I don't think that sexual orientation automatically dictates that you are an underdog.
Again, it would be really interesting if you could provide examples of Peter Parker being "supposedly straight". I have been reading Spider-Man comics since 1988 and maybe I have missed something.
The best part of Spider-Man is that when that mask is on anyone could be Spider-Man. I think Bendis wrote about that when he introduced Miles as Spider-Man. He could be black, white, straight, gay, or whatever you want to think.