Storm- Zazie Beetz
Gambit- Nathan Parsons
Beast- Hugh Laurie
These 3 are the ones that immediately sprang to mind for their respective roles and I think they'd put in good performances as the characters.
Cyclops- Josh Dallas
Cyclops always came across as a bit of a boy scout, very by the book, very "clean" in contrast to Wolverine's rougher tougher personality, and he has an honest love for Jean. I think Dallas could pull this off, I know he was in the first Thor film as Fandral, but that was 9 years ago and the part was recast for Fandral's subsequent appearances so I don't think the general audience would remember he already appeared in the MCU.
Also I've gone for a slightly older Cyclops because I think it gives opportunity for a more nuanced portrayal of the Cyclops/Jean/Wolverine triangle (if the MCU decides to explore that) since Cyclops and Jean would already be in a very well established solid relationship by the time Wolverine appears on the scene.
Jean Grey- Rachelle Lefevre
A natural red head should be cast in the role, especially as the MCU's version of Mary Jane (an iconic red haired character) is not a red head. Again, I've gone for an older Jean Grey for the reason listed for an older Cyclops. I also think Lefevre has the look to her where she'd be believable not only as the kinder Jean Grey but also as the more malevolent Dark Phoenix.
Jubilee- Brianne Tju
Jubilee is normally portrayed as teenager so I think it would be interesting to have her be a young adult instead. She'd still have that lack of experience of life that comes with being younger but she won't be that kid sidekick character put in to appeal to children and teenagers. I think the X-Men should come in a variety of ages and from all sorts of backgrounds so whilst Jubilee would be younger than the rest of the X-Men, she's not an annoying teen.
Lila Cheney- Ginnifer Goodwin
Admittedly I'm not as familiar with the Lila Cheney character as I am with others on this list, however if she is portrayed as how I interpret she might be portrayed from what little I have read about her, then I think Goodwin would be a good fit for the role. Goodwin can give attitude and hold her ground in a believable way which would also fit with the Lila Cheney character.
Rogue- Tuppence Middleton
Probably a very unconventional choice. I know Alexandra Daddario tends to be a popular choice for the role but she always looks like she's got "crazy eyes" in pictures in my opinion. I think Middleton would bring a quiet confidence to Rogue. Given that she could kill someone with her bare skin, it would make sense that the character would want to minimise close contact with people (after taking precautions to minimise skin exposure) without wanting to become a hermit. Middleton could play that needing to distance but wanting close contact with grace and dignity without making Rogue sound like a whiner about it.
Mr Sinister- Johnny Depp
I think Mr Sinister would experiment on homeless people which turns them into the morlocks and the morlock massacre is him trying to get rid of the evidence. As such, I think the public persona of Dr Nathaniel Essex would be one of a charming man, a smooth operator and a leading scientist in the field of genetics. Depp could portray both aspects of Essex's personality whilst keeping that undertone of danger whenever Sinister is playing nice.
Magneto- Timothy Dalton or Ian McKellan
Xavier- Patrick Stewart or Mark Strong
I've said before on here how there's the possibility of running into an age issue with Magneto given the timeline of the MCU if they keep his holocaust origin story. As a result, and given the fact Magneto and Xavier were a big part of the prequel trilogy, I think their role would be minimised in the MCU. Really they only need Xavier to put the X in X-Men (which they could do within one movie) because power wise, Jean Grey can fill the telepath power role and likewise Polaris can fill in the controlling metal power for Magneto. Therefore, whilst Magneto and Xavier could appear, they could also be gotten rid of by the end of one movie which would be a bold move.
Because of this, it's tempting to just say keep Patrick Stewart and Ian McKellan as Xavier and Magneto respectively, especially as they are the right age for what the characters would be within the MCU (late 70s/early 80s/80+) plus they've proven more than capable in the roles before. However, if they did want to go with new actors and avoid using any of the Fox actors, then I suggest Timothy Dalton for Magneto and Mark Strong for Xavier.
Dalton has a commanding presence, a must for Magneto, and if they used de-aging technology for flashbacks (which would be a good way to include Magneto and Xavier within the MCU without affecting present day events) then it's easy to see how Magneto ended up with 4 kids (or at least two if Scarlet Witch and Quicksilver don't count).At 74, Dalton would be within the ballpark of the age a current Magneto would be and they could have him cause havoc for one movie (possibly two) before the torch is passed onto Polaris.
Xavier is less problematic age wise because his origin is not based on a real world event so his friendship with Magneto can feature an age gap so Xavier could stick around depending on his age. Mark Strong could give a calm performance as an Xavier who is perhaps not as wholesome as he likes to make out he is.
Pyro- Matthew McConaughey
This one is just for fun. Who wouldn't want to see McConaughey as a crazy arsonist who is happiest when he's setting something on fire. McConaughey's Pyro could be one of those characters whose minimal screen time doesn't make them any less memorable.
Wolverine- Zach Galifianakis
This one is definitely an unconventional choice but I reckon Galifianakis could surprise people. I think it's almost certain that the MCU will minimise Wolverine's role and push Storm front and centre, not only to differentiate themselves from the Fox movies (and Hugh Jackman's outstanding performance) where Wolverine was a major player but also Disney are going to want to get their diversity quota and Storm ticks those boxes (but at least does it in a way that's not forced). Galifianakis is in his 50s so could play a more grizzled version of Wolverine, he's 5 ft 7 which makes him short (especially against Josh Dallas as Cyclops' 6 ft 1) and he could give the air of someone who has seen a lot of terrible things in his lifetime. His love for Jean could be played as less of a love triangle (through would probably still be considered a love triangle) and more an unrequited longing for intimacy that he has become distanced from. He should know that Jean won't leave Cyclops for him and that she won't reciprocate his feelings in the way he'd want her too but he can't stop how he feels about her.
Polaris- Morena Baccarin or Jeanine Mason
Both women would give a different dynamic to the character, Mason could play a Polaris who is more naive, easily manipulated and emotionally led, whilst Baccarin could play a version whose a little bit tougher and genuinely believes in Magneto's ideology which would enable her transition into taking over Magneto's role. Both women could feasibly play Magneto's (as played by Timothy Dalton) daughter age wise without eyebrows being raised, the major thing would be making sure she doesn't come across as an SJW especially with her green hair. Baccarin probably has an edge over Mason in that regard, she can portray fury as more subtle, tempered but no less stubborn. It's also important that the character isn't treated as basically a gender swapped Magneto in which case Mason may have the edge over Baccarin as her version of Polaris wouldn't be as entrenched in Magneto's ideology as Baccarin's older version of Polaris would be.
Kitty Pryde- Freya Tingley
Ellen Page's Kitty Pryde was always a bit too glum and mopey so a more upbeat and optimistic Kitty Pryde would be a nice change. Freya Tingley could possibly pull that off and given that she's so short, she could also play younger than her actual age.