Its a prequel with some liberties.
As simple as that.
This.
It contradicts a couple minor details from the trilogy because it allowed for them to tell a better story. The
Star Wars trilogies contradict some minor details between each other as well to tell their stories. It doesn't mean they are reboots of each other.
When Singer came on board, he cut out Cyclops, Jean, and Storm because their inclusion in the 60's wouldn't match the trilogy timeline. The opening shot of the movie is a re-creation of the opening shot of the first movie, thus setting it in the same universe and continuity. The entire events of
X-Men: First Class stem from an incident that happened in
X-Men. Mystique's entire aesthetic appearance is identical to that of the trilogy. And while aesthetically Beast looks different, his role in the movie completely matches up with his backstory of
X-Men: The Last Stand. Even Moira McTaggert's appearance in
X-Men: The Last Stand, she is established as a "former colleague" of Xavier's, which is exactly what she would be considering their history established in
X-Men: First Class. If you're going to use her age, in a blink and you miss it cameo appearance, as evidence for a "reboot", then
X-Men: First Class is rebooting itself after the first 15 minutes, when Raven is portrayed as much younger than Charles, when in the introductory scene, Raven is portrayed as the same age as Charles.
The movie contradicts 2 scenes that combine for a whopping 30 seconds of Xavier walking, however the events of
X-Men: First Class don't contradict the actual narrative of Xavier recruiting the different mutants in the 2 different instances.
Star Wars: Revenge of the Sith contradicts
Star Wars: Return of the Jedi when Luke asks Leia if she remembers her
real mother, and Leia begins to go into detail about her real mother... but her real mother died during child birth in
Revenge of the Sith. So... did
Revenge of the Sith ignore
Return of the Jedi and toss it out of continuity because it contradicted a minor plot element? Or was it a contradiction simply for establishing the story it was trying to tell?
Star Wars: A New Hope, Obi-Won also states that he has never seen R2-D2 before, which the prequel trilogy shows us is obviously a wrong statement, thus a contradiction. And since the ages of characters is a big selling point for "teh REBOOTZ!!!1" around here, there's no way that Obi-Won would be as old as he is in the original trilogy, considering his age in the prequel trilogy. That's much more than an 18 year age difference between Ewan McGragor in the prequel trilogy and Alex Guiness in the original trilogy.
Not all movies have the air tight continuity of
Lord of the Rings or
Harry Potter... in fact, most film franchises don't. Most film franchises will have contradictions between them from film to film. It's kind of a natural part of telling stories with extended plot arcs over multiple installments. Especially in the case of
X-Men where you have 4 directors, dozens of different screenwriters and producers making 5 movies over the span of 11 years that are adapting 50 years worth of numerous comic book runs that span multiple runs, different retellings of the same stories, and retcons of their own that change it's own official continuity.
That is not a reboot. A reboot is
Batman Begins, which completely ignores that
Batman,
Batman Returns,
Batman Forever, and
Batman & Robin were even made, and tell their own story without any consideration given to the previous series of movies.
X-Men: First Class gives a lot of consideration to the movies that came before it, and establishes itself pretty blatantly within the same continuity, thus ceasing to be a reboot. It does take some liberties in areas where it needs to to tell a better story. But taking liberties does not equate to reboot.
If anything,
X-Men: First Class (and any future sequels) are more along the lines of
X-Men: The Next Generation... it exists within the same continuity (just as
Star Trek: The Next Generation exists within the same continuity of
Star Trek), but tells stories during a different time period, thus not directly connecting itself to the events of the original trilogy, and allowing itself a lot of creative freedom to tell some pretty wicked stories, without contradicting anything.