I generally accept DS9 as canon, though not many of the elements I dislike about TNG that carried over, such as the depiction of Klingons. I’m not sure if I accept Jadzia’s death and Ezri Dax’s existence as canon.
The TNG depiction of Klingons is just a slight variation on the depiction of Klingons in The Motion Picture, The Search for Spock, and The Undiscovered Country. (Except they no longer have pink blood in the 24th century I guess, and the honor culture thing gets cranked up to 11.)
As for my personal canon: TOS, TNG, DS9, the original movies (1 thru 6), and that’s it. Maybe some of the Peter David TNG novels. But none of the TNG films, no Voyager, no Enterprise, certainly no J.J. Abrams nonsense, and none of the newer post-Abrams Star Trek series either.
I’d probably want to make some edits also. It’s a little hard to accept stories like Star Trek 4 where time travel is something anyone with a starship can do at any time whenever they feel like it. I mean, that really creates a very sloppy Universe. In fact, I’d like to remove most time travel episodes, because most of them are written as comedies anyway. But things like “Cause and Effect” and “All Good Things” are fine.
I’d also like a better resolution for Gul Dukat’s story arc than just ending up as a clinically insane Satan worshiper. I get that this was thematically consistent as an antithesis to Sisko’s role as the Emissary, but whatever. How awesome would it be if instead they had a multi-episode arc depicting Gul Dukat on trial on Bajor for war crimes, like the Nuremberg trials? (And then like one of the regular cast-members could end up somehow having to be his defense lawyer.) Instead, the writers had him fuck around with some wormhole demons and then fall into a volcano or something.