Count me as another viewer who never noticed Psylocke in
X-Men: The Last Stand prior to this thread. In fact, even after she was mentioned, I still didn't remember her. I had to do a Google image search just to have any idea of where she was supposed to be in that film.
Going back to X-Men, I really don't think that Wolverine's time traveling could cause a person to be born at a different time. Its easier to just treat Wolverine Origins as either completely non canon or at least mostly non canon (the stuff without Deadpool, and possibly also without Gambit, could probably still be stuck in the time line fairly well, if you really wanted to keep parts of the movie).
IMO, it's easier to say that
Deadpool is in a different continuity.
X-Men Origins: Wolverine was clearly meant to be part of the same continuity as the other movies. They even included a brief clip from it when Professor Xavier is reading Wolverine's mind in
X-Men: Days of Future Past.
Bolivar Trask, Hank McCoy, Deadpool, Psylocke, Angel, even Sabertooth were all used as background characters (or barely coherent henchmen in Sabertooths case) and then the X-Men people went "Oops, we shouldn't have done that, now we want to use them and what we did doesn't fit with what we're doing now".
My theories:
"Secretary Trask" (the government official played by Bill Duke in
X-Men: The Last Stand) and "Bolivar Trask" (the industrialist played by Peter Dinklage in
X-Men: Days of Future Past) are not the same person. They're 2 completely unrelated people who happen to have the same last name.
The Hank McCoy that we see on TV in the background in
X2 is the same Hank McCoy that we've seen in the other movies. He's just using that mutant suppression serum that he made in
X-Men: Days of Future Past. However, I suspect that the serum becomes progressively less effective with each subsequent dose. By the time of
X2, it may only work for a few hours at a time. By the time of
X-Men: The Last Stand, it may no longer work at all.
As for Sabertooth, my theory is that, in the movie universe, Sabertooth & Victor Creed are not the same person. After all, at no point in
X-Men Origins: Wolverine is Liev Schreiber's character referred to as "Sabertooth," not even in the credits. And at no point in
X-Men is Tyler Mane's character referred to as "Victor Creed," not even in the credits.
I want to take a moment to talk about what a tremendous job the franchise has done thus far in 'matching' the younger and older actors, because it really does feel like we're seeing Fassbender, Hoult, and J'Law play younger versions of Ian McKellen, Kelsey Grammar, and Rebecca Romjin(Stamos).
McAvoy, for as good as he is, just doesn't quite have the gravitas of Patrick Stewart and so the 'matching' isn't quite as seamless, but they've made things work by playing his Xavier in a way that fits with what we know of the character from the first trilogy but lets him bring his own 'flair' to the role.
I like Hoult's portrayal of Beast but I don't think he quite has the same gravitas as Kelsey Grammer's version. But then, very few actors can match Grammer in the gravitas department.
Fassbender is even more badass than McKellen, which is a helluva feat!
McAvoy definitely puts his own stamp on Professor Xavier. But, IMO, part of what makes his portrayal so interesting is when I watch him and think of Patrick Stewart in the back of my mind. I have a hard time picturing what Stewart would have been like when he was young. He seems like one of those people that was never young, like he was born as a stately, Shakespearean 40-something. But, of course, everyone was young at some point. So it's funny to see McAvoy playing Xavier as a flirtatious grad student or an angry drug addict and know that he will eventually turn into the wise Professor that we all know.
A timeline change in 1973 achieved through time travel can account for changes in the 60s or 70s if the new timeline has someone traveling to 1960 for example that the old timeline didn't have.

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I suppose that's
theoretically possible but it also seems extremely irresponsible from a narrative standpoint! "In addition to the time travel changes that you've already seen, there were also additional time travel incursions to earlier time periods that caused further changes that we never told you about." That's completely breaking faith with the audience for a time travel story to rely on the audience assuming additional time travel that we were never told about! There aren't enough "

"s & "

"s in all of cyberspace to express myself right now!
It doesn't even require additional time travel for the "ripple effect principle" to work backwards. In the 2011 Mortal Kombat game, Raiden's transmission of a thought-projected warning to his past self creates changes that independently put a number of characters in places that they hadn't previously been in the original timeline.
How does that work? I'm assuming that all of alterations occurred after Raiden's earliest past self received the warning. Otherwise, it would seem like
Mortal Kombat is working with a very different theory of time travel than
X-Men: Days of Future Past. (I couldn't really say since I haven't played a
Mortal Kombat game since 1996. And the plot was never really important anyway.)
There is no such thing as a "soft reboot", and I wish people would stop using the term.
There is, although there are very few examples that I can think of. To start with, I would define a "soft reboot" as a movie that is primarily new but is ambiguous enough that it can fit into a previous continuity if you squint hard enough. The 3 examples I can think of right off:
The Incredible Hulk (2008). Ignore some of the details in the flashback sequences and it actually fits surprisingly well with
Hulk (2003).
Superman Returns. It recasts most of the key roles and redesigns many of the elements but still keeps distinct references to the early Christopher Reeve movies, such as the John Williams score and using footage of Marlon Brando as Jor-El.
TMNT (2007). It's so vague that you could easily tack it onto the end of most
Ninja Turtles continuities. (I like to imagine it as a sequel to the live action movies from the early 1990s.) It's so deliberately agnostic that, in the Turtles trophy room, we see the ooze canister that presumably transformed them, and the crack in the middle is strategically placed so that we can't tell whether it says "TCRI" or "TGRI."
Also,
Young Sherlock Holmes could probably fit with most Victorian depictions of Sherlock Holmes that don't specifically give contradictory information about how he & Watson first met.