Thats a slightly combative way to phrase it.
I don't think it's combative -- it's just stating what right-wing politics's goal is without using rhetoric that also justifies that goal.
In my view the key difference is that conservatives believe in Equality of Opportunity and Liberals believe in Equality of Outcome, usually referred to as Equity these days.
Conservatives believe Equity is unjust because bad actors will game the system, eventually causing the system to collapse. Thus their ideal society is one of no discrimination where everyone is given a fair shot, and the resulting hierarchy is natural consequence of a persons personal choices.
That is indeed one example of a logical syllogism employed by right-wing politics to justify a social hierarchy. But the desire for a hierarchy preceded the logical syllogism constructed to justify it.
That's the dividing line between the left and the right -- the left a priori wants equality in all things because it a priori views people as all basically equal. The right a priori wants hierarchy because it a priori views people as fundamentally unequal. You can build logical syllogisms for either view.
Now, to be overly simplistic, the real world has 3 things making that an issue, racism, billionaires, and poverty. Star Trek doesn't have any those (on Earth), thus allowing for a working system. Conveniently, Trek doesn't talk about the economy much, allowing everyone to ignore the Socialist Utopia underpinning everything.
Yep, that's a major part of how
Star Trek squares the circle of creating a future that looks appealing to both leftists and rightists -- avoiding showing most of future society and how it functions, and instead focusing on this small slice of life (a space paramilitary) while insisting that progressive politics have triumphed back home where the camera does not go.
If we were to see a series like
Star Trek: Federation President or
Star Trek: Domestic Law Enforcement or
Star Trek: Dilithium Miners United or
Star Trek: Queer as Folk, shows that depict a broader view of Federation society, I think ST would have a harder time pulling off its all-things-to-all-political-orientations trick.
Edited to add:
If you ever want to see an example of equity taken to a ludicrous level, you should read "Harrison Bergeron", a short story by Kurt Vonnegut.
"Harrison Bergeron" is a good example of why saying that right-wing politics is characterized by a desire for social hierarchy and left-wing politics by a desire for equality, is
not prejudicial in its rhetoric, just factual. Wanting both hierarchy
or equality can become oppressive.
(I would, however, argue that hierarchy is more often oppressive and more often more intensely so.)