In 2013, a young Italian girl named Sofia De Barros became the public face of an emotive campaign that called for people with degenerative diseases to be given access to an untested and controversial stem-cell therapy, which was promoted by a psychologist who claimed it could work miracles.

De Barros’s family, defended by a lawyer called Giuseppe Conte, went to court to demand that their daughter, suffering from a terminal illness that leads to paralysis and blindness, be given the so-called “Stamina” treatment, over the concerns and objections of scientists and doctors who warned that it was unproven and possibly dangerous.

One of the voices at the centre of the gut-wrenching fight was a burgeoning political party called the Five Star Movement, which had seized on De Barros’s story as an example of how Italy’s “establishment” was hurting ordinary citizens by keeping a “cure” out of reach. Stamina was “effective” and deserved further research, the party claimed in a press release at the time, because “citizens” believed that it was. Beppe Grillo, one of the Five Star Movement (M5S) founders, who has also supported unproven cures for cancer, used his popular blog to support pro-Stamina protests.

In fact, Stamina was later proved to be a con, and the psychologist behind the treatment, Davide Vannoni, was convicted of conspiracy and fraud.

The controversy came under fresh scrutiny last week after Conte, the family’s lawyer who supported Stamina, was plucked out of obscurity and named as Italy’s next prime minister by a new coalition government led by Five Star, now Italy’s largest party, and the far-right League.

Conte was chosen, despite his lack of any political experience, by two leaders – Luigi Di Maio of Five Star and Matteo Salvini of the League – because they could not agree on anyone else. Hours after Conte got the green light to form a government, chaos ensued. The two parties have been squabbling over who to put in the cabinet. One of the people Conte wishes to appoint is Paolo Savona, his proposed finance minister, a vociferous critic of the euro, which he has called a “German cage”. But that choice is being resisted by the president, Sergio Mattarella.

The development roiled Italian markets on Friday and has deeply worried Brussels, in large part because one of the few things Five Star and the League agree on is their distrust of the EU.

The wrangling appears to be centred on a disagreement on just how Eurosceptic the new government ought to be. “There is an institutional grammar that has to be rewritten,” said Giovanni Orsina, a political historian at Luiss University in Rome. “This conflict is something we might have expected, because President Mattarella – installed by the former prime minister, Matteo Renzi – belongs to the old majority and the populists are impatient when it comes to checks and balances dictated by the Italian constitution.”

The two populist parties cobbled together a coalition following an election on 4 March that resulted in a hung parliament. It plans to raise spending, slash taxes and possibly install a finance minister who believes that Italy’s entry into the eurozone was a “historical mistake”. Beyond the question of what this means for Italy and the EU, the parties’ rise to power could have a profound impact on Italy’s institutions, which have already come under attack. The Stamina episode gives a hint of what Italians – and the world – might expect.

The M5S leader Luigi Di Maio held talks on the new cabinet. Photograph: Angelo Carconi/EPA

The League was in a coalition with Silvio Berlusconi from 1994, but under a different leadership. Five Star has never been in government. They both have a long history of embracing the unorthodox, supporting conspiracy theories, and challenging institutions that have traditionally been seen as the bedrock of Italian society. Now, after years of serving as parties of “no” against the former centre-left government, Five Star and the League are in charge.

Emma Bonino, a former foreign minister who now serves as a senator for a party that supports the EU and defends the rights of migrants, told the Observer that there were plenty of elements of the parties’ joint agenda to be frightened of, especially policies against migrants. But she also noted their resistance to political norms.

“They consider the institutions to be their property. I think that this is the basic problem,” said Bonino. Asked about the Stamina episode and the parties’ criticism of mandatory vaccinations, she added: “The anti-scientific mood is very big.”

When Mattarella failed to immediately give his blessing to Conte’s nomination as prime minister, in part because questions had arisen about whether the law professor had padded his academic credentials, the move was immediately lambasted by a senior Five Star official, Alessandro Di Battista.

On Facebook, Di Battista warned Mattarella against serving as a “lawyer for those who oppose change” and on Twitter, he called on supporters to back Conte and put pressure on the president, who is rarely criticised by political leaders and is meant to be politically neutral.

Di Battista’s father also took to social media and, in an attention-grabbing post, warned that if people got angry “the palace of President Mattarella may become like the Bastille”.

In the run-up to the vote on 4 March analysts noted that in some ways both Five Star and the League – formerly the secessionist and xenophobic Northern League – sought to appear more mainstream in some of their views. For example, while both parties have been extremely critical of mandatory vaccinations, both sought to play down this position, despite Five Star holding rallies in the past that called on all parents to have a choice in whether their children be vaccinated.

Jacopo Iacoboni, a journalist at La Stampa who has closely followed Five Star, said that Di Maio had begun to present himself as being more moderate, but that he believed the populists were still wedded to their unorthodox theories, in part because it has been a strong draw for voters.

“It has been a useful way for Five Star to attack any established expertise,” Iacoboni said.