Continuity is a serious subject for all fandoms.
This is just factually inaccurate. Plenty of fandoms have a majority of members who do not take continuity seriously.
Doctor Who famously plays fast and loose with continuity all the time; other properties feature constant new versions of the story that are mutually exclusive. Fans of musical theatre productions usually have no problem with new productions of classic shows with radically different sets, costumes, acting choices, etc.
Many fans on this site will tell you that the different drawings and models of the TOS Enterprise are of different ships.
Are you referring to the reuse of footage shot for "The Cage" throughout the series, with the spikes on the warp nacelles and the lack of bulbs at the back? I've never met anyone who tried to argue that the use of the two contradictory versions of the TOS
Enterprise model meant we were seeing two different ships.
I follow a continuity that is close enough that you won't notice. Which is what you get in most TV series or movie productions. They try to get things close enough so you won't notice. Does anyone really care that Luke changes which hand he is pouring the blue milk in Star Wars? No. Because it is close enough. Does anyone really care that in a few episodes they mirrored the footage or that there are slight costume changes between shots? No. Do most fans care that there are slight differences between the different TOS Enterprises (the 11 foot, 33 inch, 18 inch, 4 inch, on screen drawings, the DS9 5 foot - an exact 1/2 repilica of the 11 foot mode, or the Remastered CG model)? No. But WTF with the Enterprise in Discovery? Sorry, but that is a reboot design.
My problem with this argument is it suggests that there is a degree of variation that can be accepted via suspension of disbelief and a degree of variation that cannot. But where does that border lie? How can that border be universal?
It's better to just err on the side of suspension of disbelief.
Anyone who cares about continuity is calling it a reboot.
You can care about continuity in the sense of finding reconciling contradictions a fun game, yet not call it a reboot. That's what I do. I mean, DIS Season Two is set something like eight years before TOS. Who's to say that the
Enterprise didn't undergo a refit between series?
And yes, fans do have a say in the matter.
I mean, this goes back to "Death of the Author" vs. Authorial Intent. Fans get a say in how they
interpret the text. But they don't have a say in what the text actually is. The text is that DIS and TOS are set in the same continuity.
Now if you want to say, "I acknowledge it's all set in the same continuity and that the creators just want us to suspend our disbelief, but for my personal enjoyment purposes, I pretend DIS is a reboot," that's fine. That's legit. Because that would be acknowledging a subjective interpretation of the text that contradicts the text for your personal enjoyment. But trying to actually re-write the text -- to claim that the text is that DIS and TOS are in a different continuity when the text is clearly the opposite -- is just ridiculous.
Fans get to interpret the text. They don't get to
write the text.
Things that don't fit cause endless hours of discussion to try and find a reason for it.
Or until fandom just decides to stop acknowledging the contradiction and collectively agrees to pretend it all fits together irrelevant of the text. "James R. Kirk," the "time barrier," the lack of women in the service, and "UESPA" vs "Starfleet" are all clear contradictions within TOS or between TOS and later ST that have no actual explanations, but fandom just squints and pretends the contradictions don't exist.
But the remastered version of TOS adhered to the 11 foot TOS Enterprise design with variations for the two pilots and the differences in the model when they were originally produced. The HD version of TOS shows the original design in The Cage and that is canon. So WTF is the design in Discovery? It isn't canon.
Yes, it is canon. Because "canon" is the body of intellectual property owned by someone upon which derivative works are based. The "canon" of the
Sherlock Holmes series consists of all of the novels and short stories about Sherlock Holmes written by Sir Arthur Conan Doyle --
even if some of those stories contradict one-another. So it is with the DIS version of the 1701. It is canon -- whether you like it or not.
You don't get a say in that. Only ST's owner, CBSViacom, gets a say in that. If CBSViacom decides to de-canonize DIS tomorrow, that is their right as the owners of ST. But you and I? We get a say in how we
interpret the discontinuity within canon, but we don't get a say in the existence of the discontinuity within canon or in what constitutes canon. The canon is defined by CBSViacom and no one else.
But Discovery breaks continuity in every way that we nerdy fans have appreciated of all the prior productions.
People said the same damn thing about ENT, and the same damn thing about TNG, and the same damn thing about TMP.
When you break continuity to that degree, you have created a reboot.
No, because you as the creator get to decide that it's all the same setting even if there are contradictions. How many children had Lady Macbeth? The text contradicts itself, but that doesn't mean Act I of
Macbeth takes place in a different universe than Act V.
Remember: This is all make-believe. It's all the same setting if the creator says so. The contradictions only affects future stories if the creator lets them.
It is a reboot and I don't really care what you or anyone employed by CBS has to say about it.
Once again: If you said, "I personally treat it as a reboot for my own interpretation purposes but acknowledge that the text indicates it is not," that would be legit. Claiming that the text says something it does not is not reasonable behavior.
Saying, "DIS is a reboot of ST because of the discontinuities between it and prior ST installments, and I don't care what you or CBS says" is about as rational as saying, "Act V of
Macbeth is a reboot of the universe seen in Act I because of the continuity error over how many children Lady Macbeth had, and I don't care what you or William Shakespeare says about it."
You can say it all you want, but it's just not actually present in the text.
They didn't care to put any effort into fitting in or picking a time period where their ideas would have been fresh and new.
This too is factually inaccurate. There are numerous elements of DIS that were carefully selected to reference or duplicate elements from TOS -- the sounds of equipment, for instance, or the design of the Federation logo (meant to resemble that seen in TMP and in Franz Josef's
The Star Fleet Technical Manual).
What you actually
mean, and would be factually accurate to say, is, "I do not like the use of a different design aesthetic from what I had imagined the world of TOS ten years earlier would have looked like."
Except for the language, their Klingons could have been a brand new species set post Voyager and it would have worked the same.
You know, here's the funny thing: You and I have similar creative impulses here. I agree that the basic stories of DIS S1 and S2 could have been set in a post-VOY setting, and I would have preferred to do so because I subjectively would have preferred to keep continuity a bit tighter. (The differences this would have necessitated would have been minor -- Michael's parents would have needed to be killed in a Klingon raid during, say, the Federation-Klingon War of 2372 seen in DS9 Seasons Four and Five, for instance; Sarek and Spock would have had to have been a different Vulcan family; Pike would have needed to be a different captain; etc. But the meat of the stories would have been the same.)
But where we part ways is this: I understand that my creative impulses and aesthetic tastes are subjective and cannot reasonably be binding upon artists that have different tastes than myself. The show is being made with the goal of appealing to millions of people, not just my "has-been-a-Trekkie-since-I-was-9-and-can-recite-the-history-of-the-ST-Universe-from-memory" self.
They deliberately broke continuity in their choice of setting and design and made it a reboot.
They deliberately introduced minor discontinuities into the text, yes.
That does not make it a reboot.
As they say, actions speak louder than words and that is what you have, a very big FU to long time fans who care about such things.
Honestly, anyone so anal-retentive as to interpret an artist having different subjective aesthetics and creative impulses from themselves as a "very big F.U."
deserves to receive just such an insult.
At least not from my own perspective, as someone who enjoyed both shows to a degree. I do think ENT had issues with continuity at times, but I think many of its issues were due to executive meddling. They wanted "essential" Trek elements added in for marketing purposes, so now we had an Enterprise that seemingly never got referenced for some reason later on. VOY also had the problem of the execs wanting it to be TNG 2.0, because they understood that TNG had been successful. But they failed to appreciate some of the ways it became successful, like having good writing and acting in the better episodes.
I sort of wish it didn't exist, but that's just me. 
Having some glaring design flaws (like the turbolift caverns on both the Discovery and the Enterprise and the seemingly open space that doesn't fit the exterior hull) doesn't help, IMO. YMMV of course. 
