They get that shit from the same place where they get the shit that all of us queers are pedophiles.

Conservatives can't admit that they hate us and "woke" people in general just because we don't conform to their rigid ideas about how things should be, so they have to come up with and spread all sorts of completely ridiculous lies to justify their hate. They don't want to see themselves as the bigots they are, so it's nicer to have some "proper" reason for wanting to literally fucking murder us.

Generally conservatism attracts people who aren't "cognitively equipped" to deal with complex situations. Their ideology emphasizes strict hierarchies and roles because they need a simplified and predictable society so they can function. That's why conservatives literally fear people and things that are different from what their mental model says they should be; being different makes them unpredictable, and possibly a threat. Ditto for why they usually cling to very literalist interpretations of their religions.

And I'm not just pulling this out of my ass either, there's tons of research on it. See eg. this list for sources