How exactly would Reynolds’ Deadpool in the MCU work?

Off the top of my head?

To explain where the mutants come from. You could use the multiverse. Fox's X-men were in Earth-10005 after Days of Future Past the time line split and current X-men are in Earth-TRN414. Have a Multiverse Crisis where a group of X-men of Earth-TRN414 cross over to Earth-199999 seeking help. Just for a nod to comics have the team show up right where Hulk is well hulking out. Not knowing he is a hero, Wolverine attacks Hulk.

Eventually it gets settled and Cyclopes explains their need. The Avengers go back over to Earth-TRN414 and face Mr. Sinister has created and released a virus to put selective pressure on the Homo Sapiens and Homo Superior. The virus mutates and kills humans almost instantly. Most Homo Superior and Mutates (like the Fantastic Four)survive, but there isn't a lot left. The mutants and the mutates only made up 5% of the population to begin with. Earth-TRN414 doesn't have a Bruce Banner, Tony Stark, or Suri and the task of making something to stop the virus is too much for Jean (i know she's only a doctor in the movies but I liked that change) and Reed Richards to make.

As the Humans see that they are dying and the freaks aren't some fanatical humans are pushed to launch nuclear weapons. Their thinking process is fuck the muties if we can't live no one can. It turns out that Mr. Sinister is behind these guys too pushing them too it. As the Children of the Atom increased with nuclear proliferation. It would be another pressure for people to evolve.

The X-men and FF get wind of this knowing they need to stop the fanatics and if they don't succeed a place to go. Reed Richards develops a Multiverse Portal device. It can only transport a few at a time because the portal is small. For it to move masses of people a portal needs to be on both sides. Cyclopes, Jean, Deadpool and Wolverine jump through multiple worlds looking for a inhabitable one. The find Earth-199999. Deadpool when he comes through has a slew of curses that are bleeped out and he is aware of the bleeping. He takes a shot at MCU and Disney. Now audience is caught up.

The X-men and some Avengers go back while whoever is science minded and still alive after Avengers 4 work on the portal device. They defeat Sinister but at the last second the Nukes are launched. There has to be some kind of problem with the portal on both sides. On Earth-TRN414 it's a acolyte of Sinister who damages the portal machine. Whoever Hulk and Avengers were fighting when the X-men show up sabotage's Earth-199999's side too. We could have a running b plot on 199999 that would facilitate this. Both sides are fixed and in an instant all the Mutants and Mutates of Earth-TRN414 are transported to Earth-199999. The X-men and Avengers leave Sinister to be alone on Earth-TRN414.

The last shot is of people rioting and protesting the Mutants that just showed up. Have multiple news shots of it.It's been 6 months since the mass transport and people still have questions. Have shots of people asking what are mutants? Where do they come from? Why did they invade. Some people screaming NO MORE MUTANTS! Have scenes of Mutants in tent cities with masses of people around perimeter screaming and throwing things at them. Through a Fence. The last shot is of the fence bending then rolling up around the crowds of humans as Magneto comes floating into the camp freeing the people. The post credit scene you see an old man with a M stamped on his hand walking in a camp like the one Magneto liberated. He puts a hood on from his poncho. The hooded figure turns around you can only see half of his face. It shape shifts to a white face with black lips. He smiles with pointy teeth.