And given that Hawley as recently as eleven months ago was still lobbying to get permission to use Patrick Stewart, I sure as hell stand by mine. You and the 20th Century Fox execs may be of the opinion that Legion takes place in an alternate universe, but authorial intent matters. Legion is part of the same universe as the mainline X-Men films and Deadpool. Your opinion and executive meddling don't change Hawley's original intent.
Fandom today has too black-and-white a mindset about continuity, that either two works share a "universe" or they're completely separate. That's not how fiction really works, though. All fictional "realities" are just stories, and one story can pretend to take place in a version of the other's world without the other story reciprocating. TV history is full of TV adaptations/spinoffs of movies that purported to be set in the same universe as the movies but were then ignored by later movie sequels -- or that changed elements of the movie continuity to better fit the needs of the series, so that they pretended to be in continuity but actually weren't.
Continuity is just a storytelling device, like any other. It's not a real thing, just an idea that stories use in ways that serve their individual needs. Story A may find it useful to employ the pretense of continuity with story B, while story B has its own needs that require ignoring or contradicting story A. Two stories can be mutually contradictory in how they define their respective "reality," because neither one is real at all. There is no objective right answer; there's only the subjective answer of which approach is right for each specific story.
And really, the X-Men screen franchise is an odd one to attempt to apply any sort of rigid view of continuity to. The films have always been wildly inconsistent with each other, sharing only an impressionistic continuity to begin with, not unlike many movie series over the decades like Universal Monsters or Godzilla or James Bond. And
Legion in particular is a wildly surreal show that defies any monolithic definition of "reality." Even if you ignore the surrealism,
Legion has explicitly established the existence of an infinite multiverse within its cosmology, so it could easily be taken as an alternate timeline to the X-Men films, which already include
at least two timelines of their own anyway. So that allows them to share a "reality" without really being in continuity with each other. With a multiverse, you can have it both ways.
Indeed, I remember a Fox exec talking about
The Gifted in those terms, suggesting that the X-universe TV shows were parallel timelines in the same multiverse as the movies, so that they could share a lot of basic ideas and history yet still freely differ in the specifics. So they both share a continuity and don't at the same time. Which is often true of TV spinoffs of movies merely from a creative standpoint, but multiverse theory allows an in-story excuse for it too.