There is no evidence to support the assertion that rates of rape are “relatively high” in those countries. You can assume the statistics are vastly underreported—and they certainly are—but you’d have to multiply them by 100x or 1000x to reach the rates of the US. At that point you’re speculating.

The (frankly kind of bigoted) assumption here is that being well intentioned and having the “right” attitudes towards female sexuality is somehow more effective at preventing rape than strict social separation of the sexes.

And you’re correct that non-consensual sex is a relatively small factor in HIV rates compared to widespread consensual sex with multiple partners.