I think you could only watch this show in a heterosexist society - a society where your unspoken assumptions code how you hear dialogue - and then come away from it believing Hawkeye isn't queer.

Isn't that the point, though? That those who remain in an unquestioned heterosexist society think he's straight, and don't complain, while those who are reading from a queer positionality see him as queer, thus giving the show the best of both worlds by keeping both audiences?