You're mixing up a lot of things that don't really belong together here.To the broader point, Star Trek is a major cultural export of the USA, and has always shown what are now considered to be anti-right-wing ideals, from the Cage daring (by the standard of the era) to have a woman in a senior role in the command hierarchy rather than a traditional gender role, to the main series putting a Japanese officer on the bridge in the shadow of WW2 racial tension, a black woman on the bridge as a main-cast role even though US domestic politics were the Civil Rights era, and a Russian officer also on the bridge despite the US international politics being the Cold War era.
By the films (perhaps sooner, IDK I'm not that nerdy), the canon was the Federation no longer used money.
Later, Top Gun and Stargate SG-1 are both on-the-nose US military propaganda; the latter achieved success even though Sam Carter was not at all a traditional gender role, even introduced with stereotypical gender hostility before Jack O'Neill accepted her as an equal. Stargate Universe failed despite pushing the civilian scientists into military training, IMO because it was trying to be reboot-BSG with different set dressing, putting off all the people who wanted more Stargate without attracting anyone who wanted more BSG, but again, BSG itself managed to be a major cultural export despite the not-traditional-gender-role-conformant characters of Laura Roslin, Starbuck, and (even if they were not really human) Number Six and Number Eight.
In specific details of what's mixed up and why it doesn't work together:
> Yes, the "far right christian ideologies", such as masculinity, traditional gender roles, patriarchal values, self sacrifice and fighting for your kin and country, protestant work ethic and entrepreneurship, protecting your borders against foreign invaders, hierarchical social structures based on merit, the same values and ideologies that built and made the western anglo-european civilizations the envy of the world superpowers, that got us to the moon, and where the rest of the world wants to emigrate to.
Some of that is indeed far-right (masculinity, patriarchal values, and what is currently seen as "traditional" gender roles while actually missing both what those were and why they were fundamentally changed by inventions such as the washing machine and childhood vaccination).
"Self sacrifice", "fighting for your kin and country", and "protecting your borders against foreign invaders" are basically everywhere, those didn't help differentiate "the western anglo-european civilizations" from anyone else, you'll find the former in every culture we have records for, and the latter two (if you accept "territory" rather than "country") even more broadly in species whose most recent common ancestor we share was when dinosaurs still ruled the earth.
"protestant work ethic and entrepreneurship", I mean the Catholics would like a word about the former, let alone historical references like the Islamic golden age having already finished three centuries before the Protestant reformation and China being busy as the Middle Kingdom for most of world history right up until the west surprised them with the Industrial Revolution; and if "entrepreneurship" is limited to "far right" then the USSR getting to space first and China doing pretty well in the last few decades are also counter-examples.
"hierarchical social structures based on merit" covers everyone except anarchists and hereditary rule, I think?
> and where the rest of the world wants to emigrate to
No we don't.
At this point, lots of us are skipping the USA even just for holidays and business trips, let alone migration.