For some reason, everyone seems to think that just because someone is homosexual, they can't engage in heterosexual sex for the purposes of reproduction. A gay man is perfectly capable of impregnating a lesbian woman. There's merit to the assumption that the EARLIEST breed of humans, if inclined towards homosexuality, would not have survived, but homosexuality as a taboo is a rather modern development. If, at this time, heterosexuality had become taboo instead, people would STILL reproduce, they'd know better.
Think of it as heterosexual relationships being taboo, not heterosexual sex being permanently banned forever.
Imagine, if heterosexuality was TRULY considered an abomination, which is what the point of this theoretical situation is, but was required to keep the race going, it would need to be practiced, but would likely be done in very limited and controlled means. Possibly regulated by the government. Those found practicing it outside of that would suffer from the same social stigma that homosexuals do. Actually, in more medieval times, they might be lynched, executed, and sterilized.
People seem to assume that simply by breeding non-stop, the heterosexuals would be able to take power. But from a societal standpoint, they'd be oppressed and any efforts down that route would be stymied. Furthermore, they'd likely be worse off economically due to maintaining a larger family. The stigma attached with being a hetero would prevent them from obtaining any level of political power, at least in a representative government. Imagine religion promoting homosexuality because it is approved in the Bible. Christianity had a MASSIVE hold on the world back then.
Seriously, try not just taking the easy route and going "lulz gays can't reproduce they'd die". That makes it sound like you think that homosexuals as a social group in power would be too stupid to know that they need heterosexual sex to reproduce. If you think homosexuality is a "genetic" thing, then two homosexuals could reproduce another homosexual child easily. If you think it's a "social" thing, well that's even easier if society were screaming it was the norm and decrying heterosexuality.
I'm not all that fervent about this, but I'm interested in seeing what people really think might happen, rather than just taking the "I'm so snide and clever" way out.