The objective is a foothold in culture war stuff, largely around LGBT people but about other things too. The ultimate goal is to re-establish a culture where gay people are unable to be out in public, especially in places where there are children. This means no gay teachers. No gay characters in media. Websites with LGBT content being treated as pornographic and requiring age verification.
The narrative is "look at these liberals forcing sex on children." Parents go to school board meetings and read passages ripped from context as lurid eroticism to rile up their neighbors. If normies go along with this "think of the children" stuff then it becomes a foothold to the next steps. We've seen this trans people, where bigots have successfully converted "this is about girl's sports" into policies banning healthcare and safe bathroom use.
At this point it's extremely clear - objectively, by counting criminal convictions - which demographic is a real danger to kids, not just sexually but in many other ways.
And it's very much not the writers of books with LGBT content.
I can understand why the real culprits might want to deflect attention from their moral failings onto others, and why pointing out the facts might make them very, very angry.
The narrative is "look at these liberals forcing sex on children." Parents go to school board meetings and read passages ripped from context as lurid eroticism to rile up their neighbors. If normies go along with this "think of the children" stuff then it becomes a foothold to the next steps. We've seen this trans people, where bigots have successfully converted "this is about girl's sports" into policies banning healthcare and safe bathroom use.