I am sorry, but I have so little sympathy for entitled fan behavior at this point that to me this is more an argument in favor of defying continuity, rather than against it.
I'm not sure that's really fair, is it? I think you're confusing toxic fan behavior, which can take many forms, with what people like.
I am quite sure that there are things that they could do to Star Trek that would have you up in arms that fall under "continuity" or "canon" that you don't even think about.
What if they had a show that retconned the Klingon Empire to be a pacifist, hippy race that went around the Galaxy spreading good vibes?
What if they they said that, in fact, Jedi were in Star Trek and that all of Star Trek really took place in a galaxy far far away a long time ago?
What if the whole story about Picard was that he had been secretly molesting all the kids on the Enterprise, and that this was just a show about his trial?
...the whole thing about certain IP, from Star Trek to Buffy to anything, really, is that part of the appeal of the IP is the comfort, the continuity, and the canon that it represents.
There will always be a push/pull between innovating new things and respect/continuity with the old. Because if you have no respect at all for that which came before, you might as well not be using that IP at all. If you don't care about the canon or continuity of Star Trek at all, why bother making it a Star Trek show?
In short, this is dangerously close to William Shatner's "Get A Life" speech from SNL, except without any of the humor.