I would stand to gather that there are just as many fans who think that Discovery isn't good Star Trek that felt the same way about...
- TMP ("it's so sterile!")
- TWOK ("it's so militaristic!")
- TNG ("why is the captain bald... and BRITISH?")
- DS9 ("to boldly stay put!")
- VOY ("its TNG lite!")
- ENT ("prequels suck!")
- Kelvin Trek ("it's all action!")
Sure, the internet amplifies the argument. But there's no real empirical evidence to suggest that there's truly any more people out there that hate this iteration of Star Trek than any other. They're just louder. MUCH louder.
Conversely, there is version of Star Trek that can appeal to different groups of people while retaining a similar ethical core.
TOS: campy, Cold War era action with extensive critiques of American foreign policy
TMP: 2001-style cinematic experience
TWOK-TUC: interpersonal relationships; considerations of aging and mortality, meaning of friendship, obsession, prejudice; light-hearted critiques of modern society and religion; considerations about reaching across the barricades
TNG: living a philosophical life
DS9: political ethics and the problems of Realpolitik
VOY: the dedication of a leader to the well-being of the community
ENT: the newness of discovery; the disappointment that comes from one's life course changing
Kelvinverse: comradery; the need for sacrifice; willingness to put one's life into the bigger picture
Discovery: the importance of group identity; resisting expediency
Everyone can have some version of Star Trek that appeals to them. Being an historian by training and profession, I identify mostly with DS9. I doesn't bother me that others take to other series (although I'll argue which is better, like any geek).
The funny thing is that the Discovery crew were themselves discontent with fighting a war. It was not the thing that they signed up for, and they did not feel that fighting was central to their identity or their goals. The resentment was something that put off some people who were looking for a TNG-style crew that never fought. However, it was a theme that comes down through strong, perhaps most strongly in something Miles O'Brien said: "It's not you I hate, Cardassian. I hate what I became because of you."