Democracy would collapse as any sort of meaningful political ideal.
When certain individuals are clearly superior(with both the brainpower and strength to back it up) why would they want to obey the powerless masses? Even if the Prof. X's of the world would submit to it, the Magneto's wouldn't.
Exactly. That's why I sided with Senator Kelly in the first X-Men film, for example. How can there be any privacy in a world where telepaths exist? And how can you protect against characters who can shape shift (impersonating anyone they want) or walk through walls (thus being able to steal whatever they want)?
The simple fact is, people who can do anything will do everything
. The existence of mutants would only make the problem worse.