There does seem to be a general tendency of "If you're not a good looking guy, you look like a molester".
Good gods, I have twice had the police called on me for such a reason. Because I have a beard, and due to Asperger's I have some strange tics, people are apparently convinced I'm a predator. The first time was when I was fucking sixteen! Thankfully the officers themselves were good people, and weren't suspicious of me at all.