As previously stated LGBT people already seem to genocide themselves.
They increase their own risk of death in a multitude of categories and can't reproduce.
So how have they not already gone extinct?
Because, as with the theories on evolution of homosexuality, it's some complex genealogy that causes it. I mean if you want I could summarise them for those that don't know them. But, essentially you can't get rid of them, and we've been trying for at least a thousand years to no success.
Sociological theory (I know I know just listen) would support early intervention and support for fags which would essentially turn them from faggots into normal people that have different sex lives.
Unfortunately for the planet, the most expensive, time consuming resource dependent and pussy ass methods are almost always the correct ones.