There has been a lot of talk about the FOX/Disney merger and how the characters owned by their respective companies would be brought into the MCU after being seemingly absent the entire time. I am just putting out some ideas as to how they could be introduced.
One way that they could be introduced is by having mutants exist as long as humans but are only coming out now because they had a reason to.
What Marvel could do is have them be around for nearly as long as the human race, but they didn't expose themselves. They would be terrified of their powers when they manifested, so they kept it a secret to insure that the people on the street didn't find out. But the mutants with physical differences (like Big Foot) isolated themselves from society and were only seen a few times by small groups of people. Mutants would be a something that only conspiracy theorists believe exist. Anyone else would just say they don't.
Professor X this entire time was actually finding kids who were "different" and taking them to his school for gifted youngsters. The X mansion could be around long before the MCU started, there just wasn't any reason for them to make it public knowledge. Until now. During or after the events Avengers 4, the X-Men realize that they can't keep hiding forever and that they need use their powers to protect the planet. They could have Professor X send them to fight and help the Avengers with some sort of threat.
They would make themselves public say that they have been around for many years and explain how they got their powers. This would make more mutants all over the world feel that they can go out and show the society who they really were. But the problem with that is people became scared when random people from a "new" species just started coming out of the wood work. They would view them as a threat to humanity despite them having protected them. Which is why they fear and hate mutants.
I like this idea because it stays true to the X-Men mythos at large. Wolverine and Magneto still had their childhood trauma and Professor X has still been accepting mutants into his school for years. The mutants can have their powers for the same reason, a certain gene in humanity has evolved to the point where it created a new species. It also keeps their dynamic with humans the same, mutants can be seen as a rival species while mutation could be seen as a disease. They could introduce a few X-Men members briefly in one movie and expand on them in the next.
This all works because it makes the X-Men work in the MCU just like it does in the source material. It also explains why we are only now seeing mutants.
But what do you think?