No offence, but the point where it gets sticky is when this neat split-up real men - real women (talking of behaviour, thinking, attitudes - not what organs they have) is hailed as something objectively right, something carved in stone, or in DNA, for all time. Real men are hunters, short-tempered, competitive and want to rule things alone, they don't sob and they never accept close friendship from a woman if they think they can have sex and want to. Real women are nurturing, a bit emotional and guilt-ridden, care about their looks and put hubby's career and the kids before their own job.
I don't think most gays, lesbians or other erotically "non-standard" people wish to make everybody else become gay, or insist on that men should always stay at home with their kids and should be ashamed if they are fast-paced, competitive and gritty. What gays, dykes and trans people etc want is more, like, the right not to be slammed with "you're not acting like a real man/woman" from a hundred newspaper columns, ads and books, from everyday talk too, and then get branded as misers or, again, not-real-so-and-so, if they try to pitch a discussion about why it's like that. In a sense, many gay men probably want gayness to be a non-issue in society, or at least a non-sexual issue to the people they don't choose to have sexual relations with, but that's a long way off. And this becomes all the more striking because you can't, in pretty much any country, define yourself as midway between man and woman and make the world around you buy it: the gender identity, and the many correlates of it in behaviour and styling (do you wear a skirt? perfume? are you likely to cry if you're very afraid or moved? will you plan the weekend for the family and make sure things run smoothly?) even if constructed have to be pretty definite on the surface, or it will just get confused.
Since sympathetic gay men (I'm using it as an instance of "non-standard males") were all but absent from, like, mainstream movies and tv until around 1980, this idea that "real men are hot-blooded womanizers or John Wayne types" can look all but self-evident. But there's nothing objective about it.