As any Catholic master of ceremonies will tell you, it takes only the tiniest sartorial mishap to lend a Python-esque flavour to moments of the utmost solemnity.

On 1 July the rebel traditionalist Society of St Pius X (SSPX) created four new bishops in defiance of Pope Leo XIV during a five-hour open-air Latin Mass in a Swiss alpine meadow. The consecrating prelates wore dark-red velvet chasubles over scarlet-and-gold dalmatics with matching gloves. They descended from their thrones bearing sacred chrism. Afterwards the new bishops stood in a row, mitres perched on their heads for the first time.

Liberal bishops wear stumpy headgear. ‘Trads’ favour gleaming skyscrapers

For traditionalist Catholic bishops – whether they are cardinals loyal to the Pope, prelates of tiny rebel sects or, like the SSPX, somewhere in between – size matters when it comes to mitres. Liberal bishops wear stumpy headgear scarcely distinguishable from tea cosies. ‘Trads’ favour gleaming skyscrapers that look magnificent so long as they fit properly.

That was the problem. Two bishops wore their Shard-shaped mitres at a jaunty angle; one gust of wind and they might impale a worshipper. The others were taking no risks. Older readers may remember the 1960s comedian Freddie ‘Parrot Face’ Davies, who jammed his bowler hat down so low that his ears stuck out. That was the unfortunate effect.

Mainstream Catholics had fun with this on social media, but on Saturday it was the SSPX’s turn to snigger. Pope Leo, who the day after the consecrations made clear that all six of the Society’s bishops were excommunicated, together with any priests who failed to reconcile with Rome, pointedly spent 4 July at Lampedusa, gateway and grave of illegal migrants. Here he clambered awkwardly on to a rock (‘you are Peter, and on this rock I will build my church’), whereupon his skullcap flew off like a frisbee.

I shouldn’t be flippant when, in theory, the fate of hundreds of thousands of souls hangs in the balance. But the history of relations between the Vatican and Écône, the SSPX’s Swiss headquarters, is comically convoluted. The Society has been half-in and half-out of the official Catholic Church ever since its founder, Archbishop Marcel Lefebvre, rejected the Second Vatican Council’s ‘heretical’ ecumenism and what he regarded as the new Protestant form of Mass.

In 1988, just when a deal seemed possible, the haughty but indisputably holy Le-febvre rejected an offer that would have brought the SSPX back into the Church, free to celebrate the old liturgy so long as it paid lip service to the Council. Instead, he consecrated four bishops, for which schismatic act he was excommunicated along with the new bishops. At the same time, however, Pope John Paul II seized the opportunity to create the rival Fraternity of St Peter (FSSP), which allowed priests to use only the old Latin missal so long as they didn’t repudiate Vatican II.

After Lefebvre’s death in 1991, both the ‘rebel’ SSPX and the ‘loyal’ FSSP unexpectedly prospered. In an attempt to end this People’s Liberation Front of Judea-style rivalry, Pope Benedict XVI lifted the excommunications of the four bishops. But the SSPX was now split between moderates and conspiracy theorists who believed that the new Mass was a Masonic charade, and so there was no healing. Then along came the Machiavellian Pope Francis, who inexplicably preferred truculent Lefebvrists to loyal Latin Mass Catholics. He granted SSPX priests permission to solemnise marriages and hear confessions. As a result, even cardinals could not agree whether the Society was in schism.

And now? On the face of it, last week’s excommunication of the Lefebvrist bishops, together with priests and lay people who stubbornly ‘adhere’ to the Society, draws a red line between the Church and the rebels; SSPX priests can no longer validly conduct weddings or grant absolution. In practice, everything is fuzzy at the edges. In the past few days the Vatican has offered SSPX priests a route back to full communion which involves signing a document committing them to recognising the Council. No one has a clue how many will accept the offer.

As for lay people, there is no such thing as formal lay membership of the Society. Estimates of the number of Catholics who support the Lefebvrists range from 100,000 to 600,000 – a vast disparity that reflects confusion about what it means to ‘adhere’ to the rebels. If you continue occasionally attending SSPX Masses, are you excommunicated? Almost certainly not. But if you stubbornly insist that only their Masses are valid, then you probably are, having committed what Pope Leo calls ‘a sin of extreme gravity’ by tearing the seamless garment of Christ.

SSPX priests can no longer conduct weddings or grant absolution

It’s a mess. Even so, some of the fog is clearing from the battlefield. I was in Rome just before the consecrations; the traditionalists I spoke to were startlingly hostile to Lefebvrists whom they’d previously regarded as honourably separated brethren.

‘They tell the Pope they’re taking this step with deep sorrow in their hearts,’ said one Vatican insider. ‘So why are they issuing a limited-edition commemorative wine set with “bishop-themed labels” to celebrate their own excommunications? Why are the new bishops flaunting coats of arms, some of which display a feeble grasp of heraldry?

‘Above all, having kept quiet about Francis’s flirtations with heresy just because he was nice to them, why have they chosen to lob a hand grenade into the Apostolic Palace just as Leo is trying to put an end to the factional nastiness encouraged by his predecessor?’

It’s a good question. Although standing on a rock at Lampedusa was hardly a subtle piece of symbolism, it did remind the SSPX that, as supreme pontiff, Pope Leo can throw grenades back at them with infallible accuracy. He may, for example, decide to lift Francis’s malicious restrictions on the celebration of the old Mass in the mainstream Church, thus removing a major incentive for traditionalist Catholics to attend Lefebvrist chapels. We shall see. He’s hard to read, so it would be foolish to make predictions about the precise status of the old liturgy a year from now.

Even so, one thing seems clear. The leaders of the Society of St Pius X, having tried to make a virtue out of defying the Holy Father, are heading towards the fissiparous demi-monde of schismatic Catholic sects. This is not what their founder intended, it’s not what many of their ordinary supporters want, and the inevitable cat-fight between factions will make them thoroughly miserable. But at least they can drown their sorrows by reaching for a bottle with a bishop-themed label.