The X-Men cannot appear in the MCU' due to proprietary rights being owned by 20th Century Fox.
Captain America: Civil War is set to release in less than a months time. The internet is currently being bombarded with fan questions and theories, speculating on what motivation will drive the film. It's obvious that the film will focus on Captain America, but as to how the Civil War will conclude is up to debate. Another question on people's minds is how and where are the X-Men in all this? Yes, their property rights are currently under 20th Century Fox and Captain America: Civil War is packed with superheroes as it is, but where would the X-Men fit into the Civil War conflict if they were given the opportunity to appear? Their Marvel Comics' counterparts have members of the X-Men and other fellow mutants on opposing sides, just as members of the Avengers find themselves in Captain America: Civil War. It's not impossible to think that in the near future 20th Century Fox will come to an agreement with Disney and Marvel to share the properties of the X-Men, and fellow mutants. Fox is down to only having proprietary rights over the X-Men out of the Marvel franchise; the rights to Daredevil, Punisher, Ghost Rider, and Blade have all reverted back to Marvel and Disney which is leading toward the inevitability of the X-Men becoming a part of the Marvel Cinematic Universe. If and when this agreement will be reached is still unknown, but it brings up an intriguing question as to how the X-Men would fit into the Marvel Cinematic Universe. Were the X-Men to be brought into the MCU' as it's currently facing the fate of Captain America: Civil War, the mutants of the X-Men could have an interesting role in the MCU' just as their comic-book counterparts played crucial roles in the Civil War event as well.
Marvel Comics' Superhuman Registration Act and Mutant Registration Act
As the Civil War event began in Marvel Comics', superheroes and enhanced individuals became divided in the conflict. The Superhuman Registration Act was implemented immediately after supervillain, Nitro caused a massive explosion that killed the entire team of New Warriors and some 60 civilian children. Some saw that government registration was necessary for policing rights as well as accountability, but others had their own agendas in mind. For the mutants, it was a difficult debate to weigh in on. The Civil War event which pushed forth the legislation for the Superhuman Registration Act(SRA) to be enacted was preceded by the Mutant Registration Act which required the same of mutants to register with their governments. After the Mutant Registration Act(MRA) came into effect, there was the occurrence of M-Day where 90% of mutants were left unpowered by Scarlet Witch altering reality; termed Mutant Decimation.
Last living mutants, their part in the Superhuman Civil War.
After that event, only a small number of mutants were left on the planet and resorted to living at the Xavier Institute for their own protection. Among those at the Xavier Institute, Scott Summers(Cyclops) and Jean Grey protected the 198' living mutants living at the mansion. Scott Summers, the current leader of the X-Men did not want to involve the mutants in the Civil War conflict as he felt his people had suffered enough. Members of the X-Men stood on opposing sides regardless. Both Cyclops and Wolverine felt that the Superhuman Registration Act was another government ploy to oppress anyone in the world with power, enhanced superhumans. Thus meaning members of the X-Men who'd been in contention with another became aligned for a similar cause, although Wolverine did assist the government in their tracking down of Nitro after his explosive act incited the legislation of the Superhuman Registration Act. However known X-Men, Bishop saw that the Superhuman Registration Act was necessary to allow the X-Men their policing rights in the world. Bishop even went on to hunt down mutants who'd "escaped" from the Xavier Institute because any mutants outside of the Xavier Institute were required to have a tracking chip implanted in them. Fellow mutant Mister M, and a few others removed theirs, then proceeded to leave the Xavier Institute. Another group of mutants divided on the Civil War conflict. It appears that the X-Men house of mutants were just as divided in the Civil War conflict as fellow members of the Avengers are. Not only were the X-Men having to answer to the Superhuman Registration Act(SRA) as well, but the associated team of X-Factor was the only mutant team protecting mutant ghettos and Mutant Town in New York. All powered mutants were confined to the Xavier Institute but depowered mutants still resided in public areas like Mutant Town where they were subjected to prejudice and violence by local communities because of their mutant genes.
The X-Men choose sides.
Apart from their proprietary rights forbidding the X-Men from appearing in the Marvel Cinematic Universe, the X-Men having to choose a side in the Civil War conflict would appear much similar to what is going on within the Avengers' team. Core members would be divided based on personal philosophies, while individual members could see the necessity in (SRA) to prevent war; Marvel Comics' has mutant Bishop as the biggest mutant proponent behind the Superhuman Registration Act as his character is from the future wherein Bishop knows that refuting the idea of the (SRA) would lead to a timeline similar to the events in the "Days of Futures Past" series. As for the core group of X-Men, they're likely to be split down the middle. Scott Summers and Jean Grey's comic-book histories have them as neutrals in the conflict but if they're faced with the likes of Iron Man and War Machine at the foot of their doorstep, demanding that all the mutants at the Xavier Institute register, a fight would probably ensue. Not to mention Professor Xavier having something to say alongside his fellow mutants. Wolverine wouldn't stand for required registration either, although Wolverine(Logan) would see the government's point of view of superpowered individuals going unchecked being a liability for the world which could put him on an opposing side to his fellow mutants. He'd likely defend his mutant brothers and sisters from the prejudicial legislation of the (SRA)Superhuman Registration Act but it's plausible that he'd side with Iron Man in the conflict to end the Civil War as quickly as possible when Wolverine(Logan) knows that the potential casualties could be that of his friends. Beast(Hank McCoy) would also be a proponent of the (SRA), seeing a way for mutants to be recognized among the rest of the society is the first step in the way of acceptance among them. Beast's philosophies would probably play heavily into his decision on what side of the conflict he stands on. Among other X-Men, Storm and Kitty Pride(Shadowcat) are more likely to stand on the side of anonymity, alongside Captain America. These X-Men are just alike many other mutants in the Marvel universe that have been subjected to prejudice based on their mutant biology. Known X-Men, Storm, Nightcrawler, Kitty Pryde, and Beast have all faced some type of ridicule from the public community based on their mutant biology, and having faced that type of public reaction, these X-Men know that being publicly identified in the Superhuman Registration Act would only result in attacks being made on the X-Men and fellow mutants. They're likely to stand with Captain America. To sum it up, from the core group of mutants, the X-Men, Bishop, Wolverine, and Beast would be likely proponents of the Superhuman Registration Act, standing alongside Iron man to enlist the world of enhanced individuals. On the other side of the conflict, we'd see Scott Summers, Jean Grey, Nightcrawler, Kitty Pryde, Beast(Hank McCoy), Professor Charles Xavier, and Storm joining Captain America's team of Avengers fighting for (super)human rights. Just as in their comic-book iteration, the X-Men would likely be divided in the Civil War conflict, as any team is likely to be in a philosophically driven conflict.
Those are just some of the core X-Men and how they'd probably fit into the Civil War conflict. Have any suggestions or opinions on which other mutants, X-Men, would be standing alongside either Iron Man or Captain America in the Civil War conflict.
Captain America: Civil War premieres in less than a month, May 6, 2016.