FWIW, this was the same thing that homophobes were doing to gay people.

It’s not based in evidence or logic.

Could be that phenomenon (illusory correlation?) where there are a few rare examples of someone who is [sexual minority aka. gay/trans] is also a pedophile, and that particular example of a crime becomes prolific…but the general population doesn’t have any experience with [sexual minority] people. So they assume that being [sexual minority] means you also have pedophilic tendencies because that’s the only connection they know thanks to that prolific crime.