Trek always had to soft-sell some of the socialist ideals (e.g. "we don't need cash" without really explaining how things really do work) and then also a lot of science fiction that was popular in the more literary side of things during the 80s was actually frighteningly right-wing.
There's not really a good version of conservatism that works in this modern era, especially when you come to where the parties are staked in the US, but even in general. You can't have a modern society with all of the complexities and interrelations and cost and then have it be entirely hands-off conservative capitalism. This is why even when you talk to people who are nominally part of the right wing and actually go through the checkboxes of things that they must necessarily adhere to, you see a lot of people who are so-called RINO people ... and then a bunch of weirdos who nobody likes.
The brain's got a bunch of structures probably to prevent us from spiraling into depression when we were hunting the African savanna when our buddy got eaten by a tiger and there wasn't anything we could have maybe done about that that cause today's cognitive dissonance.
So basically the only way you can get a frighteningly actually unpopular platform through the electorate is by taking advantage of cognitive dissonance. Because you have to project this idea that a fundamentally backwards idea is going to move us forwards somehow.
If Copyright hadn't been extended for so many centuries, Trek characters would already be in the public domain and we'd see them fictionally used much in the way that we use all of the characters from actual public domain works. Shakespearean heroes, for example. But, even as things are now, the characters of Trek have had such a presence in the media scene that they do kinda take that aspect on. Thus, basically repeating the plot of part of the Babylon 5 episode "The Deconstruction of Falling Stars" where you have the crew of Babylon 5 being used by a new fascist empire being holographically simulated to say 1984-esque things... one of the weapons to maintain a state of cognitive dissonance is to go back and kinda put fascist words into leftist mouths.
So it's a bit of an accident on the part of the person, who is being dragged along politically, but it's very much part of the conservative movement to "reclaim" old media and the relatively milquetoast treatment of alternatives to capitalism and a complete abandonment of queer issues in middle-era Trek makes that kinda easy, which I guess is why NuTrek does go through some pains to state things a bit more forcefully.
I feel like Starfleet in Trek accidentally but directly led to the modern US Space Force.