Everyone is trying to be reasonable here in regards to mutants/registration/powers/etc. so let me jump in with the crazy.
If mutants emerged on Earth with powers approximating what we see in X-Men, then IMHO the powers that be would see them as the existential “other” threat they’ve craved since time immemorial. Instead of the threat from outside (aliens, for example), every government on Earth would have a unified threat from within to join forces against, especially in this modern age of 24 hour news cycles. Of course, some would try to harness the mutants for their own ends, so at best we’d be looking at another Cold War - an “arms race” where it’s a matter of who has the most powerful mutants in their arsenal. The main difference would be that, based on the distribution of mutants, former second- and third-world countries might have instant parity, if not supremacy, against former first-world powers. The balance of power would shift in a seemingly random way, that would turn tensions into conflicts that could well turn low-intensity conflicts into globe-threatening warfare.
It would be bad, very bad, and it would escalate rapidly. I don’t know if full-scale global mutant warfare could be avoided, but that’s just my opinion.
If history has taught us nothing else, it’s that militaries will go to absurd lengths to get a competitive edge, including seemingly insane things like mind-control experiments, suicide bomber dogs, and engineering super-soldiers. Actual, honest-to-goodness super-powered mutants will be militarized faster than you can say “Donald Rumsfeld”.
Although, if some are on the level of Prof X/Magneto/Phoenix, they can literally become their own nation if they want to get organized in that way. The Great Man theory of history may evolve into The Great Mutant theory, as the philosophical leanings of the highest-level mutants will determine where the world goes, be it fractured into rival warlord kingdoms, or maintaining close to the current nation-state power structure, or enforced but brutal order on the scale of nations, continents or even the world. Or maybe some anarchical post-apocalyptic wasteland.
The main issue is that the most powerful X-men mutants are virtually gods, and with any sort of support structure (i.e. not able to be assassinated in their sleep), they would have a profound impact on global affairs, and geopolitics would look nothing like it does now.
When it comes to conventional means of wrecking havoc, we typically control the means instead of the people. The government does limit your freedom when it come to possessing nuclear technology or biochemical weapons for example. You can be quarantined against your will if you are infected with a dangerous pathogen. The problem with superheroes is that they are the means of destruction themselves, so the issue becomes more complicated. It’s not a simple problem to solve.
Well, in line with the “villains that make sense thread” this should be “It’s not a simple problem to solve in cultures that like to present themselves as respecting human rights.” Take that off the table…
Declaring war against mutantkind or the equivalent is a poor idea if the mutants have a good chance of winning. And really; if mutants act like real people and not characters and you threaten them with enslavement or extinction, it’ll be someone like Magneto who becomes their leadership figure, not Professor X.
