There is no Cerebro with the opening title. But in the final battle of X-Men: Apocalypse, a Cerebro door opened on the mental plane to let Jean in. Once the Phoenix was let out of the box, there was no way it could be contained any more.
Furthermore, the X-Men title features a weapon used by the villain. The Phoenix Force in Jean plays the role of both hero and villain in this feature, and was shown to not be controlled by anyone, so while it occupied the titles there was no Cerebro to match it.
It has been confirmed that after the events of X-Men: Apocalypse the X-Men have become national heroes which basically confirms where the X-Men comics appearing in Logan came from.
The X-Men being seen as heroes in general, even after all the destruction and death Apocalypse caused, makes sense when you consider that in the past films, no one ever really saw or witnessed the X-Mens heroic actions. In the first X-Men, it was safe to assume people believed the authorities stopped Magneto due to Xavier keeping the X-Men secret in the original timeline. In X2, while they did convince the president to not blame Mutants for Stryker's actions, it doesnt seem like he mentioned the X-Mens role in stopping him, and even in First Class, Charles erased Moiras memories so she couldnt tell the CIA the team's role in stopping Shaw even if she wanted to. However, in X-Men: Apocalypse along with stopping Apocalypse, it is likely Moira told her superiors the role the mutants played (if Magneto's HeelFace Turn being mentioned is anything to go off of) and along with Charles's more militant Character Development, its safe to say he has made sure the team operate as openly as possible.
In Deadpool 2, Wade and Weasel arent really surprised to find out that Shatterstar is an alien from Mojoworld, which is weird at first until you remember that Dark Phoenix is introducing the presence of aliens into the X-Men Cinematic Universe for the first time.
Kurt's rage towards the D'Bari that killed a MCU soldier seemingly came out of place, but if you watch X-Men: Apocalypse and his scenes in this film, you may realise that he doesn't see any deaths, only the aftermaths. Throughout the two movies, the deaths he was somewhat involved in before that particular soldier were Alex, the Weapon X soldiers, Angel, Apocalpyse and Mystique.
Alex's happened while Kurt went with Scott, Jubilee and Jean to a mall. He only learnt about the death from Scott and Jean's reaction, so all he could do was pray.
When Weapon X had his rampage in the compound, slaughtering all the soldiers firing at him, the gunfire caused Kurt to avert his eyes. Hence, Weapon X's bloody carnage was unknown to him.
Angel's had him teleport the X-Men from the jet they were on to kill Angel, but the strain of his teleporting powers left him comatose for the rest of X-Men: Apocalypse's final battle. That means that he didn't see Apocalypse's disintegration by Jean using her Phoenix powers, and only woke up after the battle ended.
So, he would react with utter rage when he is too late to stop one of the D'Bari from tapping the soldier's heart and twisting it, despite Kurt teleporting the soldier away. Not only is he reacting to seeing death play out in full for the first time, he is frustrated that his powers weren't enough to prevent good people from dying.
As this film is said to follow the original Dark Phoenix saga more, one must wonder whether Apocalypse's final words ("All... is revealed...") meant that he has witnessed an apocalyptic being more powerful than he, and is rejoicing in her having the potential to destroy the world.
Selene is described as being unhinged. The full moon has been thought to cause unbalanced behaviour and insanity in people.
Hank's reaction to Raven's death might be extreme, considering that he wants to kill Jean for something most of the team acknowledge was an accident, but consider how often in the comics Beast has discussed his fear that he will lose his intellect as his body mutates further. Add in the fact that Hank's 'beast' state here was caused by his use of Mystique's DNA and it's not impossible to assume that Hank saw Raven as his 'mate' on a deeper, primal level, with Raven's death driving his feral side to take control while compromising his human mind. As a result, if Hank hadn't been stopped, he may have killed Jean while acting as the beast before he calmed down enough to acknowledge as a man that Raven's death wasn't Jean's fault in that sense...