I mean the Bell Riots happen in 2024 in the Prime Timeline. The 21st century sucks in Star Trek. Eugenics wars, Sanctuary Districts, WWIII, fascist dictatorships using soldiers addicted to drugs...
It's only after a nuclear holocaust that humanity is reborn into their "hopeful era". I mean hell, they literally had to retcon the timeline because the 90s weren't actually as awful as the show claimed and they had to move the Eugenics Wars. The 21st century is dark in the Prime Timeline, and it's fully believable that it was just as bad as our real 21st century or worse.
So no, as easy as it is to cave to doomerism, I think the message of Star Trek is that this too shall pass. Stuff sucks, no doubt, the world is in a dark place right now, but that doesn't mean it will stay that way.
I like to rewatch DS9: "Past Tense" sometimes because it really hits home how bad things are, but also gives hope for how maybe there's a future in which we look back and wonder how things got this bad.
But all of this is either compatible with a conservative reading, or requires more analysis than most conservatives are putting in. I mean I doubt Musk read the Picard books.
But then you go on to mention stuff like family tradition, which is literally a key value for conservatives, especially when it involves joining the military.
Or people being well fed, or valuing self-improvement? Think about all the rightwing grifters who go on about self improvement all the time, or how they claim that communism killed 15 vigintillion people from starvation and only CAPITALISM can feed the world. Conservatives don't want people to be starving, starving citizens are the sign of a poor society. It's okay that the Federation doesn't use money because it is post-scarcity thanks to replicators, a technological solution to the issue of feeding the poor. This is perfectly compatible with the techbro mindset that tech is the solution to all our problems, and isn't challenging to those who believe that socialism is impossible without advanced post-scarcity technology.
What I'm trying to get at is that all the aesthetics are there for a conservative to read it in a way that is compatible with their ideology, in much the same way that a liberal will read it as a triumph of liberalism or a leftist can interpret it as socialist. It isn't challenging to those ideologies, because it's vague enough and alien enough to not map 1-to-1 onto any modern political system.