House of M — I maintain that this storyline makes the most sense for the as-of-yet untitled Avengers 4. With Disney’s acquisition of Fox, they’ve regained control of the X-Men and Fantastic 4 film rights. And, understandably, they’ll want to make use of them ASAP: introducing the insanely popular characters into their shared cinematic universe as fast as possible so that they can make as much money as possible off of them when their own movies hit theaters in the next couple of years. To that end, House of M is the most organic-feeling way for them to introduce a whole new cast of X-characters without stopping their narrative momentum dead in the water after Infinity War.
House of M was a crossover event in Marvel’s comic book line by which Scarlet Witch — who notably already exists as an Avenger in the MCU — suffers a mental break and uses her insane, reality-warping powers to recreate the world around her so that her kind — that is, mutants — are the dominant species on the planet. As far as MCU canon is concerned, Wanda and her brother Pietro are the only “mutants” in existence (the product of Hydra’s experiments with the Infinity Stone left behind in Loki’s scepter after the events of the first Avengers), but we do see events in the Infinity War trailer that could suggest that this event is the inevitable result of Thanos’ arrival on Earth.
The big reveal (which, to be fair, seems much to good a twist to spoil in the movie’s first trailer) is that Vision — who had started something of a tentative romance with Wanda — is killed by Thanos when he removes the Mind Stone embedded in his forehead. It doesn’t take much narrative gymnastics to see where this event could result in a mental breakdown for her character, and that stopping Thanos might result in her temporarily in possession of the Infintiy Guantlet: a weapon that makes its bearer omnipotent. Combine the two with her desire to see her departed brother again and Infinity War‘s direct sequel could see her creating a world with more people like them — mutants — who subsequently cross over back into the MCU proper when whatever storyline they set in motion is resolved at the end of the film.
Secret Invasion — The latest rumor to hit the internet is that Avengers 4 will make use of one of the set of characters that had previously been locked away from MCU, owing to being lumped in with the Fantastic 4 film rights. Namely, these are the Skrulls: shapeshifting aliens who use their fantastic powers to infiltrate other species and take them over from within.
The comic storyline Secret Invasion saw Earth’s mightiest heroes and organizations infiltrated by the shapeshifting Skrulls and the question of who is or isn’t a Skrull agent in disguise became of tantamount importance. It’s a perfect excuse to cathartically kill off (maybe even recast?) any number of older characters, only to reveal that the “real” versions of the characters are alive and well at the very end of the film.
Avengers v X-Men — Subtly’s great and all, but sometimes you just want a good old fashioned showdown. That’s basically what The Avengers turned out to be. That goes double for Captain America: Civil War. If Marvel finally has access to the characters they once sold to Fox, why not announce their presence in the MCU in the biggest, show-stopping fireworks display imaginable?
It’s the perfect thematic segue for the franchise into the X-Men’s core tenant: that they are hated and feared by the world at large and are constantly at odds with the establishment because of it. The Avengers have already fought mutants before (Scarlet Witch and Quicksilver) and are no longer the independent, para-military, extrajudicial organization that they were before Civil War. If the world mistrusts mutants — as is inevitably going to be the case — the Sokovia Accords might force the Avengers’ hand into action, especially if certain nefarious mutants are thrown into the mix.