Why would there be gender-segregated dorms in this world?

Remember also that the girls' dorms are magically protected against boys, but not conversely (at least in Gryffindor, at least midway in Harry's career). IIRC, Hermione derides the rule as old-fashioned (but then, she's Muggle-born, so that proves nothing).

Unless they're trying to deliberately encourage homosexuality in teenagers as a strategy for avoiding accidental teen pregnancy.

A wise strategy, I would think. One reason why teen pregnancy rates are higher in the more relgious areas of the United States?

This would also explain Lupin's possible attitude (though I may be misreading) that homosexuality is a thing for the young, while adult relationships tend to be heterosexual.

This was the attitude of the classical Greeks (and then Romans), at least for men.