Eden's gate isn't a commentary on the "far right".
I'm gonna preface this by saying that lets try to keep this completely in terms of the game.
But yeah this cult is not in any way far right extremists and actually preaches things that are far more in line with whats defined as left wing ideologies - that dosent make them a far left wing cult neither and they are against everything going on in the outside world and created their own society... But still almost everything they are preaching about and the whole "community" feel they have going on and what their bunkers is build up upon is clearly a lot more left leaning than right wing in their ideologies, and they are against everything in their own society and country which again is directly opposite to a nationalist or right wing as these happily would pride themselves on their own country wanting to proudly defend it actually like the resistance in this game does. Furthermore listen to Joseph's outpost preachings, read the Book of Joseph and get a look of their ideologies and how he build up the cult - He talks about how he despise his own country, complaints about consumerism or capitalism, and talks about the "arrogant skyscrapers in the big cities" with the "greedy government who doesn't care about poor people left out by the society". He talks all about "helping and accepting the people neglected or dismissed by their country" and he works towards creating a big community with a lot of people together and dependent on each other... They openly in several monologues bashes the person in charge and openly despise right wing ideologies. Also "Faith" and her whole hippie character about finding you inner peace and using drugs to hide away from the "evil world and harsh reality". She is literally a drugged up pacifist hippie who lives inside a fake "paradise" preaching peace and pacifism which is also the direct opposite of right wing logic...
The resistance terms the cult "hippies" a lot of times and are a lot more how you would define "right wing" Americans. Many of the resistance characters are "right wing" stereotypes like the Drubmans, and Adelaide also directly calls the peggies out to be "flag burning socialists". But also generally the resistance in the game are a lot more like the typical right wing with the whole "oh yeah murica, we want to protect our land with guns horrah".
If the cult in the game were supposed to illustrate a white supremacist or far right cult, they would have put actual focus on it and not put countless of things in game to say the opposite like literally for starters for instance NOT having literally 50% of the cultist members being black people and never have the antagonists saying anything remotely racistic or priding themselves on right wing ideologies - such is literally the main traits of white supremacists or far right...Only Jacob can have a logic remotely more towards the right but not necessarily at all... The other antagonists says and preaches about things which are a lot more towards left leaning ideologies. The lead writer also stated in interviews that this cult isn't a right wing cult but "gains members from all sides of the spectrum" They are just against the government and outside world generally.
As a non American, it seems like a lot of the people who claims that the cult is a "far right" are just biased people who just wants to shoot their political opponents... Because there is literally nothing or very little in this cult which objectively can be paired together with right wing ideologies.
TL:DR This cult almost couldn't be more far away from being far right wing extremists. Like where do people even get this from unless they out of bias just terms everything religious as right wing? While it is true that religion often can be paired together with some right wing ideologies, it is not in any way a definition of being right wing especially not in a cult where a lot of people aren't actual religious but just parrots their leader and again has created their own society away from the outside world.