Like everyone else I've had thoughts about Disney buying Fox, and Marvel getting back Fox and the Fantastic 4. Integrating those properties into the MCU will be an exciting challenge; Fantastic 4 could be pretty straight forward so I won't look at that much here. I had some thoughts on how mutants could be brought into the universe and how mutation could be explained. How it works, and why it hasn't been heard about much until now. It struck me that some pieces are already in place to do so.
One source is actually outside of the MCU, but could (and may be) acknowledge in continuity: Deadpool. When Wade is recruited into the program, the process Ajax describes involves needing to trigger the latent mutant genes in his DNA by subjecting him to trauma.
My takeaway from this is that people could have the X-gene but not necessarily mutate on their own. This would make mutation more of an epigenetic event than the Fox movies portrayed it in the past. This could mean that there are people in the MCU who have the X-gene but aren't necessarily mutating.
An in-MCU example that I think goes along with this is Scarlet Witch and Quicksilver; while so far their powers have been attributed to the Mind Stone, that has never made great sense to me. Their powers have no correlation to the powers of that stone, or each other. I think the stress of the experimentation simply triggered a mutation that was already present in them both.
The next source that came to mind was Iron Man 3. There is a scene where Killian explains to Pepper that the human brain has an "empty slot", which is where Extremis embeds itself and allows powers to manifest themselves.
I've always felt that is a plot point that could have been further explored when it came to explaining the different methods individuals have used to gain powers (Inhumans, Science-based, etc).
My thought is that the X-gene fills this slot naturally, and a sufficiently stressful event is required to activate this portion of the brain. This provides a plot point that could be explored in potential X-Men movies which would deal more directly with trying to cure or prevent mutations. This could also explain how someone like Charles Xavier could connect easily with all the potential mutants when using Cerebro; he can sense this filled slot in people's minds.
HOW THIS IMPACTS PAST/PRESENT/FUTURE MUTANTS
I think that Deadpool's explanation of how to trigger Wade's mutation being adapted to the MCU makes a good deal of sense, as it opens the door to the occasional mutant popping up in the past at sufficently important periods (WW2 for example), but they would be rare enough to have been kept hidden or have their exploits be lost to history. While Captain America was seen as a publicity tool, someone like Wolverine would have been used on more clandestine black-ops missions that the public was never made aware of.
This also opens the door to a sudden influx of mutants following the conclusion of Phase 3, which is surely to be a globally traumatic event which could trigger latent mutations existing in people all over the planet.