Firstly, I still see people people confused as to how Kitty has the ability of time-manipulation. For the record, we don't need to say she has this power only out of plot-convenience. We know already Kitty has the ability to phase through solid objects on this plane of reality, she can phase through space. Now, the fabric of reality is woven by two parts, space and time. (that's why its called space-time). Its not hard at all to say if she can phase through space, she can phase through time. The question is no longer, "Can she phase through something?" It's closer to "WHEN does she phase through it?"
Secondly, on a quantum level, time travel is inherently, well, finicky. "(Dr. Who fans, "Wibbly, wobbly, timey-whimey stuff."). Most physicists in this field will happily tell you they have only the feeblist grasp on the notion, so a lot of the questions we have here are not going to have logical answers, and what answers we do have are going be inherently counter-intuitive.
I see a lot of people trying to break the argument down to whether time is immutable or not, over-writable or not. A lot of that depends on the perspective of the observer, the traveler, and other random factors. This is addressed in the film to Logan, "You will be the only one who remembers both histories." or something like that. So which Logan remembers which history? We could have as many as *3* separate Logans, the original Logan(pre time travel), the time traveler we saw throughout the film who has over written he past self's mind, and the future traveler who wakes up and, again, overwrites his own mind. These CANNOT be the exact same mind/person, as if they were, he would not have the lapsed memory from 1973 onward. This is why he can't remember anything past 1973 when he wakes up, but he is shown to be a history teacher, meaning that before his alternate future self woke up, his over-written past self could still remember his life before that point (with some blank spots due to the time travel)
On a whole, we can assume a great many of the events of world history from Origins through roughly X2 remain the same. However, a lot has indeed changed as far as film continuity with the revival of Scott, Jean, Beast, and anyone who we saw live through DOFP alternate future. There's also a lot that was not gone into, because certain predetermining factors have changed, such as Magneto being released early. So, the chances of an event that happens in the original timeline and the new timeline remain roughly the same as without any sort of time travel tampering, about 50%.
An example: does Fassbender attempt to attack the UN Summit as in X1? Well, we just do not know. Sure Rogue still has the streak in her hair, but based only off what we got in DOFP, there's lots of reasons why she could have the white streak. Dyed? Born that way? Stolen from Magneto as we saw in X1? Maybe even she lifted it off of Carol Danvers? We just do not know. Its like trying to argue whether or not you put on a white or black t-shirt this morning. Sure, you know NOW, as you are wearing said shirt, but in the seconds before you put it on, did you know? Maybe, but what if the shirt you wanted was dirty? Or missing? A lot of factors determine that choice, most of which we barely recognize on a conscious level.
To take this further, would Magneto still be a bad guy if his mother wasn't killed in front of him? Maybe, maybe not. What if they sent someone back in time to prevent that event? That's a reverse grandfather-paradox. (say his mother was spared, but he still became a bad guy. The question now becomes a matter of whether or not he is "destined" to be bad, or at least what the determining factor is that moulds him that way. But, what if he did not become a bad guy? What then? How far does this effect history?
The original comic did a fantastic job of this time-travel mystery by not killing Senator Kelly (who was the target, rather than Trask), only to have him pass the Sentinel bill at the end anyway, leaving open the possibility for the future to play out the same way. This is the now-called Terminator paradox, despite DOFP predating the movie Terminator by a few years. (This is most challenging. What if the Terminators succeeded in killing John or Sarah pre-birth? Then John would not win the war, and Skynet would win. But in this new future, Skynet would have no reason to send anything back in time to alter history, so John would still be born and ultimately leave open the possiblity of winning the war. In this 3rd alternate future, events from the original past would still play out, but just not the same way or at the same time. And so begins a never ending cycle of Skynet sending/not sending a Terminator through to kill John. Whether or not it succeeds is a different argument entirely.)
We won't really know what was retconned and what wasn't until time in the new First Class-based films catches back up with the original movies. We can't even say FOR SURE that the Sentinels will never be back/take over the world. What's to stop someone crazed nutjob human (Stryker, Gyrich, Humanity Front, take your pick) from picking up where Trask left off? Honestly, nothing at all. Sure, the likelihood of that happening again in cinema is slim, but taking the Hollywood factor out of this, there's nothing at all stopping the Sentinel-ridden future from happening anyway, just not EXACTLY the same.
And besides all that, we now have Apocalypse to deal with, who time-hops frequently. What if the bright, happy, shining future we caught only a fleeting glimpse of in DOFP is the foundation for which Apocalypse sets his dystopia of death? Or even worse, seeing as we know the next film is set in an alternative 1980's setting, what sort of fresh Hell will be waiting for our beloved mutant brothers and sisters? Maybe, just maybe, Wolverine will not go through the Weapon X program. (difficult to grasp, I know) But there is comic-book precedent already in place of Apocalypse giving Wolverine his adamantium skeleton as part of Logan becoming a Horseman.
TL;dr - The point I'm trying to make here is this: if for no other reason that the very same story telling plot devices that allowed us to have the ending we all felt we needed/deserved, these very same rules are what will allow Apocalypse to return to our world, what allows him to set up his own Age of Apocalypse alternate future (giving way to Cable and the X-Force). We do not have a totally clean slate, with no X-history to guide us. Nay, what we have been given is world of open possibilities, where anything can, will, does, and in some cases, already has happened.
