The way I see it, there is no one thing that will solve this issue. It would require great effort and investment from a government to achieve this. It's kind of an utopia.
1 - Education
First of all, people should know what mutants are. After they've singled out what is it that makes someone a mutant (a term that already suggests that the difference is probably genetic), this should be public knowledge.
Kids should learn in school that there's nothing wrong with being a mutant, that they're part of society. If there are bad mutants, they're not bad because they're mutants, they're bad because they're people who made the wrong decisions.
This comes as point 1 because it's the most important point. Only if everyone understands collectively that mutants are not a reason to worry can this society stand.
2 - Laws against discrimination
There should be rough legislation to prevent people from discriminating anyone for being either a mutant or a non-mutant - it should be equal. A cirminal is a criminal, regardless of his genetic heritage.
Companies should be obligated to hire proportional amounts of mutants and non-mutants to companies, and there should be no difference in benefits, salaries and anything else that might be used as an argument for discrimination.
Media should also be regulated in this aspect, in the sense that the very channels of entertainment (TV, movies, etc) should depict mutants and non-mutants equally.
It's also worth mentioning that non-mutants are already regulated. Everyone is obliged to always keep their ID's with them at all times. The only difference would be that the mutant's ID would have a few additional information, like their super power. If a non-mutant is caught without an ID, he should be liable to the same consequences as a mutant.
These laws should be harsh in the sense that whomever discriminates anyone, be him/her a mutant or non-mutant, should suffer very serious consequences (fine, jail time, etc).
3 - Capable Law Enforcement
Since there's no way to predict what a mutant's power might be, the whole law enforcement system would have to be reworked to be able to deal with super powered humans.
Police stations should have the necessary gear to deal with emergencies and combat-skilled mutants should also be an expressive share of the police force, to deal with a mad dude who can blow shit up with his eyes.
It's worth mentioning that the very law enforcement should also be under the scrutiny of point 2, in order to prevent the abuse of authority.
4 - Super Jails
Having a structured law enforcement is useless if you can't keep those guys out of the streets.
The feeling of impunity is a spark to discrimination. If a government continously fails to give a sense of justice and security to society, it will eventually be the spark to the creation of hate groups and such - which we don't want.
The government should have R&D centers dedicated exclusively to the development of new technologies to deal with mutants, both for the front (law enforcement) and the prison system, which would basically have to be custom made to the kinds of offenders that eventually show up.
You can't standardize jails. Or do you think that the same structure would be capable of locking up Superman and the Martian Manhunter?
I had a lot more ideas for this but I got carried away writing and forgot the rest. If anything else comes to mind I'll add it here.
Nevertheless, I think this post was enough to give you a glimpse of what this society should be: informed and amicable towards the differences - but harsh and equipped enough to punish whomever tries to crack its foundations.