Mutants (and super powered beings in general) on the level of the X-Men couldn't survive in a more realistic environment - that is to say an environment where messy, complicated people have these powers. It's doubtful that the physical planet could literally survive for more than a generation with mutants of the powers of the X-Men. The only reason that the Marvel universe continues to exist is because it's entirely and utterly fictional, and the writers can undo anything that they do with the tap of a key on a keyboard.
Once you put Mutants into our world, with the powers of the X-Men, our world dies. It doesn't matter what side of the fence you're on - the world is going to die. It wouldn't take a Hitler or an Osama Bin Laden or a crazy Norwegian or Pol Pot or Stalin. It would take two morons on X-Box Live getting angry at one another over a Halo argument with mutant powers, who normally wouldn't have the courage to use their power on someone they can actually look in the eye but when they get into the anonymity of the internet, gain the courage to misuse their powers. It would take a group of young mutants who bully another mutant into committing suicide in a public way, then defending themselves against the ensuing anti-bullying backlash. It would some mutant saying "I hate Nickelback so much I wish they would just DIAF when they perform at the Grammys!" and having the power to make it come true. It would take a mutant with the powers of Magma having a road-rage incident where they lost control of their temper because some idiot didn't signal when they cut into their lane. It would take the depressed, mentally disturbed teenage mutant who decides to commit suicide - but has the power of Charles Xavier, and so can cause millions (if not billions) of people to follow them to the grave. Those are what would kill the world - not the Magnetos, or Apocalypses, or Sinisters.
It will be the Youtube commenters who destroy the world. The X-Box Live trolls. The Freepers. The Fark Independents. The Bieliebers. The Nerdfighters. The American Family Association (AFA). The people who hate Anita Sarkessian and the people who defend Anita Sarkessian. The Columbine High school murders. The kid who has trouble controlling his bladder in high school who one day forgets to wear the proper diaper and wets his pants in the middle of class. Armond White. The Escapist moderator who's fed up with complaints about auto-play video/audio ads. The 12yr old girl who believes Slenderman is real. These are the people who would destroy the world. Real people. Not smart people, not stupid people. Not evil people, or careless people. Just people. Like us. People who have moments of weakness.
In the end it wouldn't matter what side of the debate I was on, or wanted to be on - I'm not going to survive to see which side is right. Maybe if we did the whole "Peace, Love, You're Just Like Me Except More Special! I Trust You." dance we might give mutants less to fight back against, and that might make us survive a few more years. Maybe if we did the "We're going to kill you and everyone who carries your genes across two generations.", we would survive a few more years because we'd be killing mutants before they got powerful enough to destroy the planet. But in either scenario the world will end. It's just a matter of time.
Given all that I'd be on the Pro-Mutant side. If I'm going to die, I want to die with a cleaner conscience. Just in case there actually is some sort of God in some sort of afterlife, I would much prefer to appear before them saying "I did not kill innocents to possibly save myself and my family." instead of "I murdered entire families hoping to remove the mutant gene from the entire gene pool and save the world, but it didn't work.".