“In the last few nights in Budapest,” mused Tucker Carlson, US rightwing media star, “I’ve run into a number of Americans who have come here because they want to be around people who agree with them, who agree with you. Do you see Budapest as a kind of capital of this kind of thinking?”

Sitting in a book-lined office, Viktor Orbán, prime minister of Hungary, agreed it was “one of the capitals” producing “very nice ideas”. He went on to praise Donald Trump as “a great friend of Hungary” and laud the former US president’s “America first” foreign policy.

The “kind of thinking” that Carlson and Orbán were discussing in a fawning TV interview on Thursday was, in their words, about families, borders and the struggle of Christian democracy against leftist liberalism. But for critics of both men, it was nothing less than an authoritarian, ethno-nationalist blueprint for the United States itself.

Carlson, the most watched host on Rupert Murdoch’s Fox News, spent all week hosting his show from Budapest and promoting Hungary as a model for America’s future. His target audience was the Trump base that turned a blind eye to his four-year war on institutions that culminated in a deadly insurrection at the US Capitol.

Just as the US left has often pointed to Scandinavia as an example of social democracy delivering public benefits such as healthcare, it seems the far right now has its own lodestar in Europe – a democracy weakening incrementally but inexorably like a slow-boiling frog.

“Tucker is using the massive platform that he has at his disposal, via Rupert Murdoch, to legitimise authoritarianism,” said Kurt Bardella, an adviser to the Democratic Congressional Campaign Committee. “It’s not speculation. The Republican party has made it very clear that their agenda is to institute an autocratic style of governance to the point where they are willing to throw out democracy when elections don’t go their way.”

Carlson, a prime time host often seen with furrowed eyebrows, open mouth and bow tie, and the prime minister of Hungary make for an odd couple. The former is a fierce critic of China and has spread false conspiracy theories about coronavirus vaccines; the latter runs the most pro-China government in the European Union and has pushed vaccines strongly.

Furthermore, Fox News rarely devotes airtime to international politics. Carlson felt compelled to explain to viewers that Hungary is a small country in central Europe with no navy or nuclear weapons and a GDP lower than New York state. But he also made clear he was not by the Danube river for sightseeing or goulash.

Orbán, who came to power in 2010, was once described as “Trump before Trump” by the ex-president’s top strategist Steve Bannon. His brand of white Christian nationalism and reflexive hostility to immigration explain why.

In 2018 Orbán described refugees as “Muslim invaders” as he defended his country’s refusal to take part in the EU’s resettlement programme. He also said: “We must defend Hungary as it is now. We must state that we do not want to be diverse … We do not want our own colour, traditions and national culture to be mixed with those of others.”

He has been an unabashed promoter of the far right idea of “replacement theory”, embracing ethnic purity over diversity and creating policies to encourage Hungarian families to have more children. (Carlson recently claimed that Democrats want to “replace the current electorate” with “more obedient voters from the Third World”.)

On Wednesday night’s show, Carlson told viewers that he had gone down to the Hungarian border and saw “order and clarity”, insisting that Orbán’s wall “works” and he found it “embarrassing to be an American”.

His claim that a border fence built by Orbán effectively ended illegal migration was corrected by Viktória Serdült, a Hungarian journalist, who tweeted: “In fact, HU police arrested 54,000 illegal migrants from January to August this year, threefold increase from 2020. That does not include the numbers that evaded arrest.”

But the gushing praise was calculated to feed the racially fuelled grievances of the “Make America great again” base, often white Christians who feel the ground shifting beneath their feet as they go from majority to minority in a diversifying America.

Robert P Jones, founder and chief executive of the Public Religion Research Institute and author of White Too Long: The Legacy of White Supremacy in American Christianity, said: “It’s right on brand in many ways for the kind of things that we saw in the Trump administration. This week Tucker Carlson explicitly referred to us ‘the danger of Christian culture being blotted out’ both in Europe and the US.

“It is really is an ethnic religious nationalism that we’re seeing here. The enemies are people who have darker skin and are not Christian. You see a lot of anti-Islamic sentiment there and a lot of closing of borders. Tucker Carlson picked up talking points right out of the KKK [Ku Klux Klan] handbook talking about white replacement.”

Orbán’s style of leadership also echoes Trump’s “I alone can fix it” demagoguery. His government and its allies have taken control of roughly 90% of media outlets, he has undermined the independence of the judiciary and he is tightening his influence over the electoral system. Last month Hungary’s parliament passed a law banning gay people from featuring in school educational materials or TV shows for under-18s.

Carlson, who on Saturday was due to deliver a speech to a conference of far-right activists, dismisses concerns about Orbán’s repressive regime as western liberal propaganda. He is not alone in his admiration for the Hungarian leader among rightwing opinion formers in the US.

But Péter Krekó, director of Political Capital Institute, a Budapest-based thinktank, said: “Hungary is the textbook case of how democratic institutions can be eroded and weakened and in some cases destroyed to an extent that it makes it extremely difficult to remove a leader, even in elections.”

In a warning to the US, Hungary did not flip from democracy to autocracy overnight; it moved step by step through chipping away at institutions and guardrails. A similar systemic erosion of checks and balances took place during Trump’s presidency and continues with his efforts to delegitimise his 2020 election defeat.

Krekó, an associate fellow at the Center for European Policy Analysis in Washington, explained: “Hungary has become a hybrid regime, or ‘competitive authoritarian’ regime, somewhere in between democracy and dictatorship but if you take a look at some subsystems like the political news of the state media, it really reminds you of the darker dictatorships.

“You don’t have the classic ways of censorship; it’s not like critics of the government are directly silenced or put in jail, so it’s not like Russia or Turkey. The government can keep control of the public space without practically having the need to exercise violence on a big scale.”

But he added: “At the same time, the nature of the regime is not democratic any more in many instances and I don’t think, honestly, that any western country should think about following this route to authoritarianism and the abandonment of democracy.

“The big lesson from Hungary is what happens if the institutional system is weakened to the extent that it’s hard to replace the leader because there are simply no checks and balances out there to counter his power. Let’s imagine that Donald Trump had the power in his four-year term to totally override the constitution – this is what happened in Hungary.”