The William Stryker in XFC is indeed Stryker Sr. as it is fairly evident by Xavier's reading his mind.
As for mutant hysteria / mutants vs humans, the fact that a handful of Soviet and US Navy folks have seen the mutants does not mean jack. The governments might have easily hidden things...
However there are a number of things that don't fit and make me scream "reboot":
1) Beast is shown in X2 in his human look (brief cameo) speaking with none other than SEBASTIAN SHAW on tv
2) Beast's furry mutation in X3 is apelike and not catlike (this means they've screwed it badly in XFC, as given the prehensile feet mutating in a gorilla would have made much more "sense")
3) Prof X walking in X3.
4) Raven never mentions her past with Xavier in any of the three X movies, and if I remember correctly Xavier does not know there's a shapeshifter in Magneto's team (he'd have developed countermeasures to detect Raven's specific brainpath or stuff like that...)
5) Moira McTaggart is a master geneticist in the X trilogy, a (very hot) CIA operative here.
6) Professor X does not remember Logan. Ok, it might have sounded foolish to have Patrick Stewart say "Yeah, I've seen the guy once, tried to recruit him but he told me to go f*** off"
7) Where have Azazel, Riptide, Angel Salvadore and White Queen gone?
8) Speaking of demon-looking teleporters, why neither Xavier nor Magneto, upon meeting Nightcrawler, remember about Azazel?