Interesting question, and one to which I’ve given a lot of thought.
There is a science fiction story by Charles Beaumont, “The Crooked Man” about just this happenstance, and I’ve extrapolated the culture in which the story takes place.
Basically, the genders live apart. The near-universal homosexuality is cultural, not biological: people believe same-sex attraction and relationships are “normal” the same way we expect Noah’s Ark monogamy as being literally divinely mandated. People reproduce through artificial insemination, the details of which were worked out approximately at the same time as our Renaissance, women still bear children, but lactation is induced in men, to be able to suckle boys, and children in general are taken care of communally. The reason why this is considered “natural” is because human culture evolves with everything else, and even though animals and primitive humans reproduce through direct intercourse, this is considered as barbaric as kidnapping brides is today.
A genteel censorship extends throughout education about most culture before the change. The dialogues of Plato are widely studied in school, and emphasis is given to those that talk about παιδεραστία. Love poems, if not in English, are translated with altered pronouns and names, Shakespeare’s sonnets are firmly spoken of as being about his love for Mr. W. H., and, when it’s simply unavoidable to talk about opposite-sex marriage, it’s brushed off as “well, they did it, but they really didn’t feel anything for each other.” Anyone in Africa or Asia who still…well, you know about them, right? But, they’re coming around…especially with our missionaries.
Which leads us to: crooks. That is, cisgender heterosexuals, which in Beaumont’s fiction, and in mine, are treated pretty much like gays were treated in the early American 1950’s. Sometimes, you get glitches in the system. People don’t always have the right hardware for the programming. And they’re worse than being persecuted…they’re unspeakable. Books about them are kept locked away in libraries, behind the desk. You only get to hear about them in abnormal psychology classes in college. You never hear them decried in sermons, because the Church of Sts. Mary & Martha or your Congregation of David and Jonathan doesn’t stoop to that sort of thing. Every so often a True Stories magazine will run an article “Thousands of Perverts Among Us”, where someone went undercover to one of the illegal clubs where men and women could talk together, touch each other, and even kiss — right in the open! Beaumont’s story tells of the dangers faced by such a couple.
What happens to them when they get caught? Well, they get institutionalized, of course. But be glad…there are new therapies that will put them right in a few years….electroshock, lobotomy, certain drugs…
Anyway, I guess that answers your question.