I think part of a good Magneto characterization is that he's given up on peaceful relations as impossible, and for good reason. Once that's believed, a strong hand is better than any politicking.
I think people would differentiate between hormone-addled teenagers with powers who act out violently from trained soldiers/scientists with powers that are part of an official organization that as saved the world. It's the difference between Colubmine/Sandy Hook and the US Military. All you need is one major mutant-caused tragedy to sell it, and mutants would be considered 'different in a bad way,' like Muslims, regardless of any similarities. Add to that a Magneto who seems to evidence that for mutants this isn't a 'phase' and you have full blown believable hysteria.