It seems to me that a lot of mutants are open, even proud, of being mutants, and a kid who is born weird or develops powers at puberty is very likely to be a mutant - so plenty of them are identifiable to be a target of hate, and there are certainly a few who bang on about being the future of the human race.
Also, I would have thought the fact they could be wandering around indistiguishable from baseline humans would make them even scarier to the paranoid.