Nothing about the show really looks like the Prime universe, so...
Let me start by saying, that, for Kelvin Timeline/Universe purposes, I like the 2 movies pyjamas (cause if we call the older shows as such, that's what the new ones also are, as "inspired" by them) and not really fond of the Beyond ones, though the Duty Uniforms(if they're considered as such), are ok, though some may find them militaristic(however these ARE action movies so it better bodes their pacing, in a way).
I don't have a problem with any changes they do, though I wouldn't personally like the "more uniform like approach" some seem to favor these days(to each their own per popular saying). I do have and been having a huge problem with the production companies AND with TPTB in general of shows that sell a product distinguished from Star Wars due to "targeting a more intelligent audience"(as elitist and snobbyish this obviously sounds), yet demanding those same fans to keep their brains out while following different iterations of the show, breaking its internal continutity for years, yet selling products that
rely on such continuity, which TPTB established and canonized, setting their rules on what is or isn't canonical info.
Yet those products they sell, they apparently don't respect, cause they easily change according to marketing or other decisions(who are oblivious to things like fashion running in circles over time, so let's make our own style and not keeep up to date with modern times just cause some think we should, cause you know,
its a show taking place in the FUTURE, so viewers are attracted to that aspect basically, not another iteration of modern times etc. for which other shows exist that can be up to date with modern reality, each and every time).
Now how you solve that? You deffinitelly don't mock them or tell them to get a life, cause that might mean NOT buying your products(eg, posters, novels, comics and all paraphernalia people buy when they are obsessed with something, which marketing btw loves to have). You can make bold decisions like rebooting it every time and admitting it, creating all sorts of parallel universes(abit ala Marvel) for the show. You can definitelly try to remaster details every time, like they've done with Star Wars a bit, when they want to change something.
You definitelly don't pretend that "hey all is ok, nothing changed" when it is obvious everything changed or most everything to make it no longer recognized by rules, visuals, behaviours that were there before. You most certainly DON'T try to capitalize on it by selling stuff about its INTERNAL history and Timeline's when you intend to break them all the time cause it fits your needs best. If you do, you are frank and say so - fans eventually respect that - and you don't try to explain everything.
I'm not a trekkie, don't have any novels or paraphernalia in my collection. I just know most of Trek(not all roughly 80% and not in so deep details). But I hate that what they do is basically a mockery of a large portion of the fans, each time they increase their hopes and then fail them. Which I just don't like to see happening. I lose respect to the people that do that, cause in my mind they fail their roles, which is not professional deciever(that, in a way is the actor's job, so the viewer can be immersed in the spectacle they are creating.)
I will not mind any changes they do if they will be frank about them. Else I'll just loose interest in this series just like with ENT which proved in its run things can be done properly(
*Edited to add: Since Coto) and people will like them, either way(even if it failed even doing things properly cause it was too late to save it, or the studios didn't want to keep a product that would do things properly as it might not have been the product they wanted to sell to the viewers). Else it will be same old, same old, fan vs fan pitting, which is absolutelly the worse thing a franchise can do. Back then it made fans enemies between them, and that's the reason it failed most of all imo, regarding ratings. Some enjoy to see those battles, they're just that kind of people I guess, they like to watch apparently "blood being spilt". I just abstain in such periods.
I think it would hurt Trek to repeat that. So it's not late to start thinking over their actions abit. It's good to have Trek on small screen again, but quality is something that derives from all aspects of a product.
However that's my opinion. (Apologies for being long with it, but these are things I kept to myself for a long time and feel they had to be expressed somehow, so someone knows some people may think likewise).