According to "contractual obligations" from FOX Studios, the X-Men won't be a part of the MCU for another three years. The contract's details state that if Marvel wants to use a character that showed up in one of the FOX X-Men movies, then they have to use the original actor.
So, if they want to use Wolverine, they must cast Hugh Jackman. This is why Patrick Stewart reprised his role as Professor Xavier in Doctor Strange in the Multiverse of Madness. All is not lost, however. This doesn't mean mutants can't appear in future MCU films.
Recasting X-Men is off the table, but mutants can still appear in MCU
Fans have already seen mutant-kind hinted within the MCU. First, Professor Xavier appeared in the second Doctor Strange film. More recently, mutants were alluded to in the Ms. Marvel finale, with Kamala Kahn being a mutant rather than an Inhuman. According to Devin Faraci, via Cinema Sangha:
Despite the introduction of mutants at the end of Ms. Marvel, there's no mutants in Phase 5. I know why. I know why there's no mutants. I know why this is going to take a while. There might be individual mutants, there might be other characters that show a certain interest. The reason why is the contractual situation with the original FOX is going to be in effect until 2025. So, if they don't want to use those actors, then they have to wait until that contract all expires.
Black Panther: Wakanda Forever will introduce Namor, the Sub-Mariner, to the MCU, who is Marvel's first mutant. It's unknown whether he'll be referred to as one in the movie, but the door is most certainly open.
There's also news that the first movie about mutants won't be a variation of X-Men like Uncanny X-Men; instead, it will be titled The Mutants. While some fans across the internet had adverse reactions to the rumor, there is some precedent for it. Stan Lee's original title for the X-Men line of comics was The Mutants. Marvel's publisher at the time, Martin Goodman, rejected the title:
I wanted originally to call them The Mutants and he said, 'you can't call them The Mutants' and I said, 'why not?' He said, 'our readers, they aren't that smart.' He had no respect for comic book readers. He said, 'they won't know what a mutant is.'
Well, I disagreed with him, but he was the boss so I had to think of another name. So, I went home and I thought and thought and I came up with the X-Men and I mentioned it to him the next day and he said, 'that's okay' and as I walked out of his office I thought, that was very peculiar. If nobody would know what a mutant is how will anybody know what an X-Man is? But he had okayed the name and I used it.
While we might not see the X-Men recast anytime soon, we may still see some of the original actors reprise their roles in different parts of the multiverse. That doesn't mean we won't get new mutants either. Characters that haven't appeared on the big screen are fair game if this news is true.
That means Marvel can use Fantomex, Armor, Hope Summers, and many more if they want to. Gradually introducing mutants throughout several movies is probably ideal, especially since they haven't been a big deal in the MCU yet.
Marvel could easily wait until Avengers: Secret Wars to reveal the majority of mutant-kind. That would be the ideal project to completely reshape the MCU and make all its characters fit cohesively.