What is important is clarity: the debates such as those surrounding ENT or DSC occurred because Star Trek had adopted a principle where by the time of TNG at least, TMP was definitely not a reboot of TOS, and TNG certainly not one of the films (what with all the reuse).
The reuse was for budgetary reasons, which has nothing to do with continuity. Lots of sets, costumes, stock footage, and other assets get reused by different productions in separate continuities, like when season 1 of
The Incredible Hulk built three episodes around stock footage from the Universal movies
Earthquake, Airport, and
Duel, or when
Lost in Space, The Twilight Zone, and other shows featured Robby the Robot from
Forbidden Planet as a character or prop.
Indeed, Harve Bennett and Nicholas Meyer did consider
The Wrath of Khan something of a soft reboot of TMP, tacitly ignoring it while not overtly contradicting it; the only reason they reused the sets, miniatures, etc. was because of the film's low budget. And Roddenberry considered TNG to be a soft reboot as well, a chance to cast aside those bits of past Trek productions that he was dissatisfied with or considered inauthentic. It was only after he was gone that later producers started making more explicit ties to Trek's history.
The only thing that dictates continuity is
story, not visuals or props or costumes. If two stories say they're in the same reality, they are even if they redesign every set and prop and costume, like
Discovery has done. And if they say they're in different realities, then they are even if they use the same sets and assets (for instance,
King Kong and
The Most Dangerous Game were filmed on many of the same sets by the same actors and production crew, but they weren't meant to represent the same characters or locations).
Imagine if Bryan Fuller had thrown things into sharp relief by saying in 2016 already that the Timeline, the basic events would remain Prime -- whatever happened in 2256 more-or-less happened in everyone's vision -- but that the "Abramsverse" has been formalized into the "Abrams universe" (to allow for the Prime Kelvin in the same basic style), and that the new show would be set in the "Discovery universe". There would still be minor debate on what exactly can be shared between universes, but that would be resolved more easily by comparison.
It's not the responsibility of storytellers to quell audience debates; heck, if anything, the more people debate a story, the better, because it means you've got people talking and thinking about it and paying attention to it. So creators shouldn't be afraid to let audiences disagree with their choices, nor should they let their fear of audience reaction get in the way of telling their stories the way they need to be told.
And again, design is not story. Design is the choice of individual designers and producers. Besides, Bryan Fuller had no responsibility for the Kelvin films, because he wasn't involved in their production, and they were made by Paramount and Bad Robot while Fuller was working on a CBS/Secret Hideout production.
On a related note: I lean towards Social Media giving a disproportionate voice to those who feel that way. If Discovery were actually as hated as those YouTubers make it out to be, evidence of that should be seeping through into here. The Disco Forum should be a total War Zone complete with five moderators, threads being closed left and right, and infractions being handed out like candy. That's what it should look like. Yet it doesn't.
That ties in to what I said before about evolving media giving new platforms to people like that. 15-20 years ago, those hardcore haters would've been posting here and creating the kind of chaos you're talking about (although they still would've been a small cadre of bullies drowning out everyone else and pretending to represent the majority), but these days they take it to YouTube where they can monetize their ranting.
