In my mind SNW is definitely an alternate timeline from TOS. There are just too many contractions that drive me nuts otherwise, like:
- Starfleet encountering the Gorn, Trelane, and the Metrons years before TOS.
- Spock's vastly different characterization, to the point of him having romantic relationships with not one but TWO of his shipmates and publicly talking about them in a documentary by someone he barely knows.
- Chapel having a completely different (but better, IMO) personality.
- Kirk, Spock, and Scotty all knowing and working with a descendant of Khan's years before "Space Seed."
- Uhura, Chapel, and the rest of the Enterprise crew being familiar with T'Pring in SNW when they'd obviously never met in "Amok Time."
- Kirk sharing several adventures with Pike and his crew before "The Menagerie," as opposed to just meeting him once before.
- M'Benga somehow going from CMO of the Enterprise in SNW to just a staff doctor in TOS.
- The Enterprise of the 2250s having an experimental holodeck that is nearly indistinguishable from TNG's holodecks.
- Kirk's brother Sam serving aboard the Enterprise, not to mention him going by the name "Sam," a name only Kirk called him by in TOS.
Not to mention all the other contradictions that SNW carried over from DSC, like the crew encountering Harry Mudd year before Kirk, the Klingon War, Spock having an adoptive sister we've never heard of before, and Pike knowing about his fate years before it happens (another change that I've enjoyed).
There's also trivial stuff that contradicts minor bits of trivia in TOS or TAS, like Spock never mind melding with a human before "Dagger of the Mind," there never being a mutiny on a Starfleet ship, or Robert April being a Black Admiral instead of a Caucasian Commodore, but honestly, those don't bug me too much.
But yeah, those are a LOT of inconsistences to swallow.