There have been a lot of good answers here so far, but I'd like to point out a few additional avenues that people haven't considered.
Superhumans are a lot more dangerous than you think
Nobody's perfect. Everyone has a bad day, lashes out in anger, does things like hit a wall or throw things across the room to vent. Even people who have great anger management often had to learn this skill.
A lot of the arguments over mutants being "dangerous" in works like X-Men mostly involve cases of outright evil mutants using their powers for law-breaking purposes. The perennial argument is "what if someone with Kitty Pride's powers were evil and just decided to phase into a bank vault and take all the money. What people don't often seem to consider is that all mutants are potentially dangerous because everyone has moments of emotional vulnerability, and even a slight lapse in control can result in people dead. In real life an angry dispute that leads to a fistfight or a person kicking something in anger in a world with mutants ends with a massive explosion or somebody having a hole drilled in their body with lazer eyes.
And what if you have a mutant that has some sort of mental disorder, like borderline personality disorder, schizophrenia, depression, or bipolar on top of their mutation which makes their moods unstable and often difficult to control? Hence, even if a mutant is perfectly friendly, law-abiding, and has absolutely no desire to hurt other people, they are still dangerous and not safe to be around.
Of course this argument is kind of bull. Anyone can literally be a threat to anyone. A big person, if they snapped, could easily overpower most other people in a rage and harm or kill them. But that big person could be taken by surprise by a person they think is a friend and have their throat cut (the element of surprise buys you like, what, 5-10 seconds in a fight?), and they die like anyone else. Or someone could just straight up poison you when you aren't looking, history's go-to technique for people who lack physical strength (hence why poison was seen as a weapon of treachery in many cultures). Society just kind of...collectively ignores the threat the people around us pose because if we didn't society couldn't exist.
The argument of mind control
A counterargument might be that "well Superman is a nice guy and paragon of morality who would never even swat an insect". Well, in a setting with mind control, it doesn't really matter. See, the funny thing about hypnotism and mind altering substances in real life means that there are really only two ways to go about it: hypnotism only works because the subject subconsciously wants to do it or the victim's normal thought process is totally gone. There is no "the mind controlee is still there and subconsciously stops themself from doing anything too evil". You could brainwash Superman and command him to go on a rampage killing millions of civillians, and there is nothing anyone could do to stop you. If you have mind control in a society of superhumans the world is your gunrack and all the people around you are your guns.
Indeed, this is exactly what happened in Injustice: Gods Among Us. The Joker dosed Superman with Scarecrow's fear toxin and caused him to hallucinate and kill Lois Lane and his unborn son, believing they were Doomsday. No amount of the power of love or a subconscious desire to not hurt his family could stop him. Or Professor X in the recent Logan movie. Due to a brain disease that he had no say in or control over, he had a seizure that caused him to lose control of his powers and ended up killing hundreds of people, including all of the X-Men against his will.
Deny job opportunities
Most bigotry in real life isn't lynch mobs and concentration camps. It's the casual, small things that add up until people are deprived of opportunities. One obvious way that mutants could be discriminated against is job opportunities.
Think of it this way. You're a bank owner in the Marvel universe who is trying to figure out whether they should hire Wolverine as a bank guard. However, you also know that mutants in the Marvel Universe seem to be targeted by Sentinels seemingly every month. If you hire Wolverine, it's only a matter of time before the Sentinels show up at your bank looking to kill him, and you really don't want your bank to be levelled in the midst of a superhero fight. The insurance premiums will be nuts. Indeed, this kind of happened in Spider-Man, where supervillains kept attacking the Daily Bugle just because Spider-Man worked there (okay, he was a freelance photographer, but he worked for the Bugle in everything but name).
But back to bank guard Wolverine. Wolverine, of course, has powers he can use to defend himself. But if he uses his powers on a potential miscreant things could get...messy, and said miscreant could turn around and sue you, Wolverine's employer, for gross negligence or cruel and unusual punishment. Gee, all of a sudden you don't want to hire a mutant like Wolverine.
And that's how a lot of discrimination works. People individually make the decision to avoid you because of seemingly logical reasons like you're a potential liability, or they have stereotypes in mind that make you seem as not worth it. Eventually you get to the point where you've been ostracized because no one will give you a break and the people in the society you belong to all independently made the decision that you're not worth dealing with. "Oh, these people should definitely not be ostracized by the community and given a chance to be treated as individuals rather than threats or stereotypes," they'll say, "it's just I don't want to be the one to do it."
Hatred from the elites
Another thing to consider is that you don't need mutants to be a threat to people in order to be hated. Throughout history, people in power have always hated potential threats to their hegemony. The samurai hated the idea of guns, to the point that part of the reason the Shogunate closed off Japan from the world for 200 years is they didn't want the peasantry getting access to firearms. In medevial Europe the born-nobility hated how the bourgeoisie were gaining enough power to challenge them. Modern governments hate tech giants like Google because they have increasing power over them and due to their nature as multi-national corporations there have less and less power over them.
Basically, the elites in society have always hated people with alternate sources of power that could challenge their supremacy and that the elites cannot dictate or control to make useful to them. Mutants are the ultimate expression of this. Their powers come from their bodies, not their wealth or their inventions, and you cannot take that power away from them or easily regulate it. Mutants represent a threat to the elite's status quo.
You could have a situation where the presence of mutants is unambiguously good for the majority of human society, but the elites still hate them because they are eroding their power base. For example, you could have mutants that could produce unlimited clean energy like the Flash or the Human Torch are sometimes shown doing, and energy companies (both fossil fuel and renewable like solar or wind) would hate them because they are cutting into their bottom line. Or mutants who have the ability to cure viruses and heal the sick and are hated by pharmaceutical companies because curing the sick instead of palliating them means they can't sell as many drugs.
In most societies, the elites also have a significant amount of control over the media. So if the elites hate mutants, all they have to do is use their influence over the media to run a smear campaign with anti-mutant propaganda and whip public sentiment into a frenzy to get mutants marginalized and hated by the common populace.
Forced mutant draft
Motherland: Fort Salem showed this aspect pretty well. Basically, in a world with mutants whatever country has the most powerful superhumans would be the one on top. It would be a Cold War-style arms race but with human beings instead of bombs. Therefore, governments would be pushed towards gathering up as many high-power superhumans as possible.
There could be a mandatory draft for mutants, all mutants are forced to join the military and serve it until they die, no ifs, ands, or buts. Many countries might pass laws making it illegal for mutants to immigrate to other countries (you might think this is silly, but countries have passed laws making it illegal for minorities to leave the country in the past like the Huguenots in France or the perennial example of Nazi Germany).
It doesn't matter if your local flying brick is a conscientious objecter, your government needs every mutant it can gets its hands on in order to maintain a military advantage over other countries. And if they let one superhuman slip through the cracks because they are a pacifist or don't want to be a tool of the government, they open the door to everyone else leaving as well, which leads them to become even harsher.