So in a recent Entertainment Weekly article Andrew Garfield says he thinks Peter should be gay. We know that isn't happening.
But it might be able to be worked around. Why not introduce Peter Parker's "Brother", Ben Reilly?
For those uninitiated, Ben is a Clone of Peter, indistinguishable in every way. Andrew Garfield would play both characters and both characters are essentially Spider-Man. Fans have a lot less invested in Ben than they do Peter, so it wouldn't be nearly as controversial if he was homosexual as well as homo-arachnid. Andrew would get what he wants, and we would get an awesome shot-for-shot remake/update of Zorro the Gay Blade starring Spider-Man.
They just wouldn't be able to reuse the line "We were once womb mates."