No offense to anyone, but honestly I'm a bit weary of reading about people being upset that the series isn't 100% what they wanted. We all knew up front that a new TV series was going to be somewhat different than what we expected. CBS has proven time and again that they don't view the latter three series (you could also argue TAS in there too since it kinda toils in obscurity compared to the live action series) as profitable or widely recognized as TOS & TNG were. If they did, then we would've seen HD remasters of those long ago despite how expensive the remastering process is. If you also factor in how the reboot franchise has sold for Paramount, it's obvious that CBS is going to think that TOS might be the better direction to go as opposed to TNG since it seems to sell better.
This naturally leaves us with the era of the 23rd century which logically seems to be more popular and has been relatively unexplored in terms of history and by extension is less hampered by canonical constraints. Fuller himself said it was the best place to fit the story if I believe. As much of a nice call-back In a Mirror Darkly was, and how beautiful TOS-R was, the general public isn't going to suspend their disbelief if a new series that's set during that time period looks like something shot in the 1960's. Sure people can forgive the fact that TOS looks incredibly bright and retro because it was a product of it's time, but it's just gonna come off as too hokey if they try to match the aesthetic. Yes, I'm a bit upset the Klingons look a little too alien, but we don't have the full circumstances as to why those changes were made and I'm willing to give them the benefit of the doubt for now.
Those are pretty much the only complaints I can see that seem to be giving people the impression that this show's a reboot and quite frankly I think they're overreacting. Even within universe, what we've seen of the sets and costumes do seem to be somewhat consistent with what we've seen in The Cage. The Color scheme was a lot of greys and blues and I think the set photos have a similar aesthetic. The uniforms, or at least what we've seen of them, seem to be an updated re-imagining of the Cage Uniforms. That's all it's gonna be guys, a slight update.