Speaking of "nonsense" . . . I mean, if I were to reply in kind, I'd ask how you even saw the different actors back then, Stevie. Maybe go back to singing about your part-time love of continuity?
Joking aside, you are welcome to spend the mental effort on active denial of the visible, audible, tonal, and storyline differences, things that go well beyond pittances like the recasting of minor characters. Just be glad the full-scale TOS reboot show folks have talked about for after SNW isn't getting made. You'd be in a real pickle trying to handwave that.
For others, such handwaving effort not only deflates any possible enjoyment of the show, but actively suppresses it. Such folks might be able to enjoy it as an alternate universe where they can take what they see as new and unique, which is literally what the producers were trying to create, visually. And they might be able to enjoy the stories shown as not 'bending canon' as one producer suggested, but creating a parallel universe where the old rules and facts need not apply. (Such folks could similarly enjoy a "reimagine" of Master and Commander set on a flat Earth just so long as the producers or other fans weren't confusing it with the original film's universe.)
Heaven forbid.
So yes, I'm sure you find the alternate reality chatter tiring . . . but get comfortable with it, because -- short of a tremendous reset button -- it isn't going anywhere. When you literally alter the contents of the universe before adding your own material, an alternate universe is all it could possibly be, prima facie . . . meaning even without the evidence of our eyes and ears backing that up.
This personal sniping needs to stop now. I realize this is a debate that nobody can really win, and I'll post some of my own thoughts separately. But I want everyone in the thread to settle down a bit.
The bottom line is, the studio sets the rules. They are the ones deciding what is and is not set within any given timeline, and their policy is that DSC, SNW etc are all set within the same original timeline as TOS, TNG etc. Not everyone will agree with that, and that's fine, but when it come to official policy, that's the policy.
If we go by inconsistencies meaning a story is placed within an alternate timeline, do we declare ENT to be in an alternate timeline? ENT introduced the Ferengi and the Borg, well before previously-established lore said they were encountered. It gave us TNG-style phasers and torpedoes. More importantly, it brought in characters absolutely pivotal to the creation of the Federation, heroes as it were, never-before referenced in any way, shape or form. Archer was critical to the Federation, and also played a huge role in stopping the Xindi, which brings up another glaring inconsistency. An attack that killed seven million people, and started a huge mission of vital importance to save earth, against a coalition of species that had never seemingly existed till that point, despite being quite the noteworthy force.
So, is ENT part of a new timeline, and who treats it as such? Then again, it wouldn't matter, the studio regards it as part of the original timeline, and whatever disagreements may be had with their view, their view is the one that counts.
I'm in my sixties and watched TOS first run. I've always rolled with the changes. Sure I might play the head canon thing and make up a reason why X, Y or Z was altered. But if the folks running the franchise come up with their own reason or no reason at all, I'm cool with it. I don't think it's generational. Some of the oldest and youngest people on the board share similar mindsets when it comes to "retcons" be it positive or negative. Those that take a literalist approach will probably balk at any changes. While those who are more interpretive are more inclined to roll with the changes.
All that said, I have zero problems suspending my disbelief that Strange New Worlds is a prequel to The Original Series. It's an updated visual aesthetic. It's not a difficult concept to understand.
Speaking only for myself, I'm in general agreement with a lot of this.

I think SNW does a pretty good job of updating many of the TOS elements, and does so far better than the early seasons of Discovery. Which is not to say I find some of those aesthetics bad either, but I totally understand the complaint that they don't look like they fit into a TOS era prequel.
I'm of the mind, personally, that it would also be possible to use straight TOS effects successfully like what was done twice in later series (in DS9 and in ENT); the argument that modern viewers would see it as too outdated doesn't really wash with me, because if that were generally true they wouldn't be able to enjoy the visuals in TOS. Every series is naturally a product of its time.
I also understand the complaint that sometimes the show runners don't necessarily have
good explanations for how visual changes and other things in modern series, and that too comes with the territory. I myself have never liked how the Klingon appearance in "Trials" was treated as if Bashir and O'Brien had never seen non-ridged Klingons, because the whole thing is rather silly and could have been ignored. But that's me.
To use a non-Trek example of crazy visual problems, one could read through some of the IDW Transformers comics. For various reasons, if you follow the issues regularly, one of the problems you notice is that the art style is seldom consistent. Characters will sometimes switch designs between issues with practically no explanation, often because in RL they had a newer toy released, and then a few issues later they'll switch again to a model that isn't accurate to their prior comic models or to an existing toy variation. There's a point in the All Hail Megatron arc where the majority of characters suddenly have their G1 style character models for a bit.
Oddly, one of the few times such a change actually had story relevance, the change wound up being unusually short despite the new form being a lot more badass. Megatron got beaten to the point of near death by Optimus, losing his G1 body, and Shockwave transferred his mind into a
sweet jet body. Megatron then had his G1 form turned into human scaled copies of his pistol mode and made sure they were distributed to humans who feared all Transformers, with the goal that Prime would either have to stop the Decepticons or fight and harm humans who were otherwise innocent. He only kept the jet body for a few issues, for whatever reason.
This isn't to suggest that the IDW stories are less enjoyable. Only that the art style can be confusing over time even to a nerd like me who's very familiar with the lore. Some of that was due to Hasbro having certain requirements related to the toys, some of it is simply different art styles by different artists.
To IDW's credit, it's not uncommon for one set of art styles to stay reasonably consistent if the same artists work on the whole arc, and their story continuity is independent of the original 1980s setting of the starting franchise. So there's no continuity problems if the story is set in the modern day and Starscream turns into an F-22 instead of an F-15. They even did some interesting visual things with
Shockwave's origins, establishing that his Decepticon form was originally a form of punishment by the corrupt pre-war Senate for leaking information to outsiders. They basically put his mind into a new, seemingly more primitive body while also severing his emotional core, unwittingly making the new Shockwave into a being of purely evil logic.