They want to shove gay people back in the closet.

They don't want their children to even hear about any gay people in history, or that another child they know is LGBTQIA+, because they think it is "perverse," and that their little darlings might get corrupted, or something.

They think of it like a disease you could catch from someone who is not a hardcore religious bigot like them. Obviously, this is not true. There is a range of human sexuality, and human expression that their religious beliefs don't allow.

They want their kids outed if they are seeking support for something they don't approve of, so they can shame them at church, subject them to lectures and "counseling from their pastors," and so they can send them to conversion camps (that don't work and are actually child abuse).