See, the problem here is that the gay rights movement wasn't much of a philosophical movement. It was a civil rights movement. This means that the members weren't too concerned about their arguments being perfect or susceptible to exploitation, but instead not being lobotomized/castrated by the state, and later not dying in droves because of AIDS, and more recently with the right to marry. So critiquing the philosophical origins of the movement doesn't actually hit the majority of the movement, but instead a couple of thought leaders that 90%+ of members haven't read nor really care about what they say. Kinsey is cared about more than Foucalt, and in his case, they only care about the science (by which I mean his data, not abstract theorizing), not his philosophy, and then only because it tracks with things they've seen in real life (most just use the scale, that's it).
Basically, this isn't marxism or CRT where the philosophical theory is vital to the movement.
As for the principle of consent being the only thing that matters, one can arrive there in multiple ways, some from postmodernism, others from the NAP. The problem of arriving via postmodernism is that not even consent really matters then, as Foucalt has no fixed morality, just whatever society says is okay is okay. But arriving there via the NAP doesn't come with moral relativism, but does come with nearly everything the gay rights movement wants (no antidiscrimination laws, but that's about it).