Are all prior Treks the same reality?
*McCoy ("Encounter at Farpoint"), Spock ("Unification"), Scotty ("Relics") and Kirk ("Generations") crossed over with TNG
*DS9 crossed over with TOS ("Trials and Tribble-ations") and TNG ("The Emissary", "Bloodlines")
*Voyager launched from DS9 ("Caretaker")
*Voyager crossed over with STVI ("Flashback") and referenced events from DS9 ("Ship in a Bottle" etc.)
*Voyager directly references time-travel events of FC ("Year of Hell", "Relativity")
*ENT crossed over with TOS (the USS Defiant appeared in "In a Mirror, Darkly", after vanishing in "The Tholian Web"), TNG ("These are the Voyages") and spun off of First Contact (dozens of references, most notably in "Broken Bow" and "Regeneration")
And following the Narada's arrival in 2233...
*ST mentioned ENT's Admiral Archer, Spock Prime's backstory consistent with "Unification"
*STID referenced FC with a model of Cochrane's Phoenix and ENT with models of the NX-alpha/beta ("First Flight") and Enterprise NX-01. Also on display was the Ringship Enterprise, which had previously appeared as background art in TMP and ENT.
*STID's Khan backstory is consistent with what we learned of the Eugenics Wars in TOS and ENT.
Each to their own, but saying the Kirk who Sisko met wasn't the same Kirk that later met Picard or who almost died on the USS Defiant which had records of Jonathan Archer's missions or that the Jonathan Archer mentioned there wasn't the same one that Riker played a holosimulation of just prior to "The Pegasus" seems to defeat the object of crossing over any of the series' at all. There are dozens of continuity errors between the different series' and movies, but IMO they're easily ignored.