sure, but you don’t insist they are the same thing.
Absolutely not relevant to the question of whether or not they respect the prior artists.
Musicians who cover songs in new arrangements can respect the songs' original artists, and the artists who make
Star Trek: Discovery have said over and over again how much they respect the artists on prior
Star Trek productions. Doing something different does not mean you're not respecting the artists who came before.
bad example, as he kept mostly the same chords and the same basic melody, only elaborating on what was already there and adding his own arrangement.
And again, he never said it’s supposed to be the same thing. There isn’t a continuity in music like there is in television.
That's the point: The people making DIS made a conscious decision not to have as much continuity in certain areas. That is a legitimate creative choice, just like doing a new arrangement of a song you're covering is a legitimate creative choice. Just because
you want continuity does not mean that those who chose not to retain continuity did not respect the artists who came before.
says who? It’s absurd to think that Starfleet isn’t open to women, even with the evidence we have in that single episode.
It's absurd
today, but the idea of women serving in the military was new when Roddenberry wrote "The Cage," and his depiction of women in that episode is still incredibly misogynistic and regressive. Remember, it wasn't until the 1990s that women began serving aboard U.S. Navy ships, etc.
Pike's line makes no sense unless the space service has been discriminating against women. If Starfleet
has not been discriminating against women, then there is no way that only one woman would be serving on the bridge and therefore no way for Pike not to be used to having women other than Number One on the bridge. The
only way his line makes any sense is if Starfleet has been discriminating against women.
Since we all agree that depicting Starfleet as discriminating against women is a bad idea, it's a better idea to just ignore that line and retcon Starfleet as having never discriminated against women, to assume that women have always served aboard Pike's bridge, and to pretend that Pike never delivered that line and is perfectly used to serving alongside women.
Which was my original point -- that a lot of stuff in "The Cage" is contradicted by later canon and/or outdated and contradicted by the value systems we have today that the creators didn't have in 1964, and that therefore it's a better idea to just ignore some elements from "The Cage" and retcon them away instead of trying to find ways to rationalize them.
). Worse, Apocalypse had witnessed the fight between Legion and a group of modern X-Men trying to stop his tampering, and Apocalypse chose to become active much earlier than in the original history.
Unlike the majority of alternate main characters that show up in Marvel, the AoA versions weren't really separate variations of the cast. They were more like the TNG crew in "Yesterday's Enterprise," in a significantly altered version of the normal timeline. The Magik of the AoA timeline never gained her set of magical powers that she had in the normal version, because she was never taken to Limbo. In the main timeline, she was one of the victims of the Legacy Virus which targeted the mutant genome and was designed specifically as an anti-mutant weapon. Magik eventually got better, of course, but she was dead for quite a long while compared to some characters. 
It's kind of like the running gag that alternate versions of Cyclops will often have his iconic visor, even though their lives are much different and they presumably don't need it the way that Cyclops 616 does. He needs the ruby lenses to filter his power because he suffered mild brain damage when the Shi'ar abducted his father, and his eye beams are stuck in an "on" state that he can't shut off. 
