Xavier intentionally kept himself and the X-Men hidden and for years and, even while speaking on mutant rights, Xavier made the decision to "pass" as a normal human. In universe, it has only been a couple of years that people had any idea that mutants attended the Xavier school.
I thought it was very interesting when Xavier went on t.v. for a debate while he was still pretending to be a normal human and the Beast joined in via sattellite. He had the Avengers logo in the background and was referred to as one of the most famous mutants in the world, the "former Avenger", Hank McCoy. And in universe that is how it is. The only known "hero" mutants were Wanda and Hank. As far as the public was concerned most mutants were villains.