In the X-Men world, the mutants are hated by most people. While I can see this happening for mutants who are physically unattractive (the Morlocks?), I think this is generally unlikely in the real world. There would be hate, certainly, but, deep down, people would idolize, worship, or envy mutants because of their extraordinary powers and, if anything, they would hate themselves for being "only normal". Maybe not to the point of brooding or suicidal thoughts, but there would always be that shadow of a thought underwriting all you do- that you exist in a hierarchy in society where you are not equal. The difference is that in the real world- even if it's a small chance- you do have a chance to be just like those people in upper society in some way or form. Maybe not a direct competitor in that you can be just as smart, but there are things you can do that are "great" in scale.
In the X-Men world, however, you either are or you aren't. And the powers of these mutants can be so extreme that even entertaining a comparison to normal humanity is charity enough for an award. Even if the world came up with a way to control mutants, this still does not erase the inherent gap between thee human being and thee mutant. For instance, you can come up with a law saying that all physically gifted people must serve in the military for life- thus bringing them under control and in service to the normal humans. But even so, normal humans would still envy great abilities of these gifted beings. This actually happened in Rome.
Rome defeated the barbarians of the north easily. BUT...they were still inherently more impressive than the Roman's. And not even in every way. They were larger, stronger peoples. A battle is a moment, but in the day-to-day you come across these people constantly and you can't help but admire them. Roman people start emulating them. They adopt them into their military...into government. Before long they are leading armies, acquire military executive positions. And not much longer then that...the barbarians are at the gates. While we may be able to overcome mutants with external tools, we can never acquire the inherent abilities of the mutants. But these mutants can learn to use our tools. They could get smarter, but you can't get taller or physically as powerful. It would be only a matter of time... If a superior form of human ever manifested in today's society, we either outright destroy it, or, in time, they will take us over.
You might think the government hates them because they would be a threat to power. Yes and no.
No power likes a greater power. I don't think any person really likes a greater power over them because it is always a threat or obstacle to their own freedom. (ironically, I think the definition of true freedom is being ultimately beyond any external force while having the ultimate ability to force ones desires on any and everything. Freedom requires that you are not restricted by any force, and that your every whim cannot be resisted by any force. Freedom is an oppressive force to anyone except the free. As a matter of logic, there can only be one free thing, ever. One thing beyond all limiting force while having the ability to force absolutely anything. If you had two, that would mean they could force each other and, thus, they would not be truly free. Am I right on that???) In the face of a greater power, the smaller will either band against it, ally with it, or serve under it. Not every mutant probably entertains the idea of political power, but there will always be those who do. Like Xavier and Magneto. Because they are so powerful, governments would not regulate them, but reform around them because governments can use them against other governments...who will be doing the same thing. (I'm going ham with all these side-theories today, but I think that all governments see things in either one or both ways; How can I weaponize it, or how can I capitalize off of it)There would be regulation, but I think it would look a lot like the regulations of western markets- promoting general order of a system while also enfranchising established markets and reducing competition from the lower markets (or lower-caste mutants). Basically, it will be the powerful mutants regulating the lesser mutants via government. That's actually what Xavier is doing in the movies. He has an idealistic, King Arthur-like vision of a world of justice, but like most ideologues, he is a sort of moral tyrant in that he seeks to enforce his will on everyone who disagrees with him. Remember, the X-Men are not saints. They are weapons constantly battling with bizarre, but lethal forces in order to defend and project the ideals of the father-figure of their organization. And no matter the nature of that organization, it is never democratic. There is always a governing center- formal or informal. It's not really much different than seeing Lenin's or Stalin's face painted on the side of buildings. The degree of control may differ, but control nonetheless. (it may be just me, but people think there is a distinction in the west because we don't follow or exhibit the traditional cues of such organizations like Stalin's Russia. But we do. We do have personality cults. And the leader's image is ubiquitous. It's just that in some places it's a singular face, but in most places, it's the most widely recognized sign of property or conquest- the flag. And if you play your political cards right, people will love and cheer the image of the leader- or flag- and die to defend it, rather than recognize it as a symbol of oppression and rule to some degree or another) Charles is constantly trying to ally with government power in order to further his aim.
People would hate, yes. But it's like our hate, today. We hate government and always have, we just have different reasons for hating and different solutions to it. We sometimes rebel against government, but there's always another to replace it and you're always paying tribute with money, labor, or life. It's not official, but in every society there is a distinction of formal or informal castes and while those on the bottom do not really like or approve anyone being on top of them if they can help it, in my opinion, that system is not maintained because we hate or reject them, but because, secretly, we want to be like them. To have their privilege and excess. To live like them. To be honored and revered and respected like them. There is convincing scientific study of human beings that suggest we are pack-animals with some sort of emphasized view of hierarchy and status. That a lot of what we do revolves around hierarchy and status. (you might have heard of that. Hopefully I don't sound to off-the-wall there...) We don't really want to break the system. We want to make our way up the system.
Why do we honor God? If God weren't powerful, would we honor him? In many ways, God and his angels represent the idealized form of man. It's what we aspire to. They are the final step in evolution as we see it. Plenty of people may hate or resent him, if they believe he exists, but if he surely did exist, no matter what, I think there would always be envy and the secret desire to be brought into the grace of power, if not being brought into power oneself. And that is why mutants would never be the under-dogs of the world as they seem to be in the comics. We would see them as the idealized form. The next step. They are super-men. Maybe for the slightest bit of time- when they first emerge into the world and there is the greatest amount of fear and uncertainty from all non-mutants we would try to rebel. But this would go away and the world would reform around a new caste of humanity. We might not like it...but it would happen.
Remember, many in the colonies or many of the constituent peoples that make up the countries of today- for the most part- did not do so willingly. They were forced into consolidated groups by the greater power, or they allied with those powers in fear of that power, or other, similar competing powers. Our own American ancestors were constantly rebelling against the centralization of smaller, local, colonial governments, and that of a federal government. And not just debates, but widespread, though scattered, insurrections. Today, you'd get the impression that people always loved being in a single government and the honor and love their nation. Not so. Back then, people loved their individual freedom and autonomy, but the smaller groups of individualists cannot compete with a greater power or a centralized force most of the time. Mutants would be that greater power. If you can't beat them, and they haven't forced you to join yet or destroyed you, join them.
Or destroy/conquer them and become the power that forces others...like the Mutants would inevitably do...either in the real world, or the X-Men.