We recently have had protest activity in the town where I work, particularly centered around libraries and schools.
This is the kind of thing of course that really is upsetting the people in the protest group, or stuff like Juno Dawson's book, or that graphic novel with the depictions of oral sex using a dildo.
Lots of the parents and some of the library staff (as private citizens) have been in counter-protest mode, and what has really struck me is that none that I talked to have really looked into the content of these things. They are being described as "LGBTIQ+ bools" and they are just accepting that description and seem to conclude that is the whole objection these people have. I think in most cases these people would not believe you if you told them what is in these books - though I also suspect if you showed them, they would feel they had to support it.
The flip side of that is the people who are upset about the books assume that all of these people, and the librarians doing the ordering, are well aware of this content and approve of it. Which is logical, but isn't the reality, the librarians in charge of collections are largely ordering based on the book filling a slot they want and based on the publishers description. They always want to find sj content, frankly I think that is more important to them than finding good stories.
But the conclusion the more naive protesters come to is that all the people who they associate with supporting LGBTIQ+ think this stuff is ok for kids and basically that they are perverts or enablers of perverts. Any concerns they ever had about gay rights look totally justified to them.