As for the "Governments are okay with mutants" stuff, they had been given the proof that it was all the fault of a lunatic racist human scientist.
With Stryker and Weapon X out of the way, pro-mutant folks in the government had an easier time pushing their agenda
I agree, and this is a pretty obvious answer. A new president also seems like a pretty silly complaint - do we have any idea how much time has passed between X2/X3 from the opening? Not so long that Colossus, Kitty, and Bobby aren't still students, but probably easily long enough for a new (and more mutant-friendly) administration.
Even if you buy that, and I don't, it's still a massive tension-killer, and an entirely boneheaded way to start what they had to have guessed could very well be the third part of a trilogy.