An OTL MAGA Republican will call the FBU whatever the conservative media ecosystem will decide to call the FBU and I doubt that "a godless communist hellhole" is going to be the word that's going to be used. I don't think the current wealthy interests behind Anglo-American conservative media in our world today is going to be interested in alienating Reds! premier capitalist superpower with more than 200 million people that has peak Scandinavian living standards, advanced science and technology, territories and military bases throughout the globe, an international reserve currency and a nuclear arsenal that far surpasses the United States of America.
Many people, Democrat and Republican alike, will see the FBU as what they think U.S. capitalism should be from different angles.
The People's Alliance is also in itself a big-tent center-right ruling party with traditionalist conservatives and rabid Cold War anti-communists inside it. The political, social and cultural establishment of the country is also going to be institutionally Tory conservative, far more conservative than the current British and French versions IOTL.
While Islam and gays/lesbians are going to be less discriminated against than OTL United States due to the different cultural contours as to "what is Europe" and the state-sponsored multiculturalism, there may be people OTL like the Tucker Carlson types that may even consider the FBU as a turbocharged version of what they imagine countries like Hungary/Russia are IOTL.
Sexual minorities, for example, are still going to be heavily repressed. The Metropolitan FBU also has an "internal colony" full of considered fifth-columnists through Franco-British Algeria. There is also a heavily subsidized set of programs aimed to keep the structure of the nuclear family unit intact with all of its patriarchal attributes. There are "drug wars" and "war on crime" campaigns and a large prison population.
The state capitalist economics of the FBU is going to be secondary to all of this, especially in our current period where neoliberalism is not even truly popular anymore.
It's also not a very good description to use especially when you have a literal "godless communist hellhole" on the other side of the Atlantic and on the other side of the Continent (UASR/USSR).
That's a generalization of an "average middle-class Republican voter" that is not even completely accurate, not to mention that you said that it's a MAGA Republican. It also completely writes off the average middle-class Republican voter as hopelessly indoctrinated to the Right whose views can no longer be shifted back to even standard New Deal economics, which they do believe if they are going to be asked about social and economic issues on a case to case basis. It has a tone of "basket of deplorables" to it.
You also underestimate other factors here beyond the narrow lens of ideology on paper, which are the material conditions of both timelines if they suddenly found each other, not to mention the class interests of the ruling class from both timelines that are going to mostly match with each other anyway.
So, conservative media is going to tell to its audience a very different tone compared to what you are imagining.
Eh, I disagree, not in the sense that they are hopelessly indoctrinated, but the reality that even if they are the premier world power, until the FBU can properly subvert and get this capitalist world into their sphere, which might not necessarily be possible given how the bourgeois are very attached to their 'rights' to massive profits, at least until the first nation to go Reds!Communist exists, then it's a tossup between further neoliberalism or relenting to the FBU line.
You have to remember that OTL is one without any actual counter-force, and while the TTL would act as one (a
big one), it would be relatively distant until they manifested in our reality in an actual revolution. The FBU would obviously be a bit more forward-thinking, but I don't think that's enough to disturb the rotting ecology of privatization, political lobbying, consent manufacturing and such. Liberty as a party in the FBU might be discredited, but on the other hand, it might be bolstered as the thing that could 'win the war' if the right grifters got a hold of it, though I see that there's probably a large contingent of people who are smart enough to realize that's stupid.
I think that the right-wing forces in the media from OTL would still be very much opposed to the FBU, and would continue to be until the FBU!MI5 or something replaces the owners with people more willing to deal with them. And that still doesn't stop the social media landscape of right-wing grifters, if anything it may bolster it, though maybe some would naturally fall into the FBU's camp but given who they are funded by, I doubt it. Even the relatively 'centre-left' media would almost certainly still oppose the FBU as they benefit just as much from the current arrangement. Neoliberalism might not be popular amongst the proles, but for now they don't have any actual power.
But what's interesting is that I think it might be a tossup if parts of grifter Breadtube (like Vaush, Adam Something, Contrapoints, etc) actually begin to support the FBU or decide to go full-heartedly with the neoliberal state department line. The FBU is arguably everything they pretty much want really, including the conservatism arguably. I think many of them would arguably become anti-communists, but whole-heartedly support the FBU as the true cause of socialism. Or they might follow the state department line and go 'well, I like the FBU's ideas, but it's clear that they have their own problems and we need to remain strong in the face of possible subversion against Washington' though of course packaged in much more 'leftist' rhetoric with many confusing segues.
I think the context for the FBU you have written is actually really fascinating so I do hope to see more stuff from you and I'm interested to see more from TTL on the FBU and the capitalist bloc!