The basic tension is the same we see in every Christian faith: what’s best? To modernise, to try to update with changing culture and social norms? Or lean in to the counter-cultural aspects of faith, to dine out on what’s different? Specifically: how far to accept gay relationships? What about married or female priests? Catholicism has so far dealt with such issues by pretending to discuss them but never changing. This was Pope Francis’s tactic: to talk the language of major reform without enacting any.

• I’m an atheist — but I saw Pope Francis as a good guy

His main radicalism lay in style. After being elected pope he wandered out without the vestments. He wore a simple white cassock, and the same cross he wore as a cardinal in Buenos Aires. He asked for the crowd’s prayers before giving his blessing. He travelled back on the minibus with the other cardinals and never moved out of the guesthouse he was staying in. Instead of the lavish papal apartment, he queued with others in the dining hall, living more like a parish priest than a head of state. He preferred a Ford Focus to the papal limo; normal black shoes, not the pope’s red ones.

This was his rebellion — “clericalism”, he said, was killing the church. Too many princes, not enough priests. A culture of privilege and detachment among leaders. He told bishops and priests to “smell the sheep”: that is, to stay close to the people they serve. He changed the tone of the papacy — but crucially, not the doctrine.

Take perhaps his most famous statement: “If someone is gay and is searching for the Lord and has good will, then who am I to judge?” It was seen to be radical but it was bang in line with Catholic teaching. For decades, the catechism has taught that gay men and women ought to be seen with love and compassion. “Homosexuality is not illegal,” Francis said. But the question is whether it is “disordered”, and whether gay marriage should be unthinkable. He never moved that line.

The Netflix film The Two Popes gives a good snapshot of his formative years and the poverty and turmoil he grew up in. It features Esther Ballestrino de Careaga, his former supervisor and mentor, a Marxist who was tortured and thrown into the Atlantic by Argentina’s military junta. He drew from her radicalism and later used it to wean Jesuits away from the “liberation theology” that had taken grip of the clergy. His alternative was a radical Christianity that crusaded for the poor but without hating the rich. Not conservative or liberal, but radical.

It always struck me as a holy smokescreen; a clever way of avoiding the Vatican’s culture wars. In effect, he was saying never mind about gay marriage. What about we clerics stop mincing about in fancy robes and get back to the streets, where we belong? He took his blend of Latin Catholicism and tried to give it general application. Standing up for the poor, the asylum seekers, the boat people — from whom, of course, his Italian family is descended.

• Who will be the next pope? The candidates who could succeed Francis

As a lifelong Catholic I ought to have taken sides in these culture wars, but I’ve never managed to summon the strength. The proof that the church is divinely ordained, I’ve always thought, lies in the fact that the church keeps going in spite of the utter dysfunction of its hierarchy. Here, and in Rome. To follow their antics (or how they handle scandals, including the most horrific ones) is to be driven to despair. I’ve always seen the church to be about the faith, not the organisation. Or, rather, the lack thereof.

Francis’s dramatic acts — turning up to climate change conventions and so on — avoided the harder moral questions. The rise of the human trafficking industry means that settling those who arrive illegally encourages more to pay to make the journey. It leads to more exploitation, more deaths. So given this, how should rich countries best discharge their moral responsibilities? If decarbonisation policies hurt the poor in taxes more than it helps them in forestalling climate change, should they really be cheered on?

His big bugbear seemed to be Latin Mass, making this one of the most sensitive and symbolic cultural debates in the Catholic church. It was the universal language of the services until the changes of the Second Vatican Council in 1965; they modernised church services, saw Latin replaced with local languages. It was seen by Francis’s generation as a kind of modernisation big bang, and the start of a trend. Might contraception be endorsed next? Women priests?

The rebellion started in the pages of The Times when Agatha Christie and Graham Greene were among the signatories of a 1971 letter to the newspaper saying that the Latin Mass was “a cathedral of text and gesture”, a spiritual treasure. Rome blinked. The ban was lifted by Paul VI, and the so-called Agatha Christie indult was born. Then, rather than die out, demand increased as more young people started to want the grit, beauty and mystery of the Old Rite. Pope Benedict then relaxed the rules further. If young Catholics preferred to say “mea culpa” to “I confess”, then what was the problem?

But liberal clerics looked on in shock at this, seeing it as an attempt to subvert and reverse their modernising vibe. A campaign was then launched for a crackdown, which Francis enthusiastically joined. Speaking in ancient tongues grated against his preference for unpretentious services. He overturned Benedict’s reforms and we’re now in the bizarre situation where Latin Masses are being held under the radar, in defiance of the church authorities. It’s the closest Catholics get to an illegal rave.

I never worked out why this needs to be a battle, but it’s one that’s now taking place in Rome. Francis became adamant about it. The old ceremonies and dress “sometimes conceal mental imbalance, emotional deviation, behavioural difficulties”, he wrote in his recent book. Or might it just be a different way of worship? This is my hope for whatever comes next: that such questions are de-escalated, and the church accepts it may never quite understand what appeals to the young.

But this takes us back to the modern versus traditionalist argument, and the Vatican tensions that at times spilt over into war. “I’m the Pope’s faithful servant,” the late Cardinal George Pell once told me with a smile, “but I’m God’s first!” I only found out later that he was the author of an anonymous tract circulated in Rome denouncing Francis’s papacy as “a disaster in many or most respects”, fixating on fashionable causes while ignoring serious ones like the fate of the church in China and Hong Kong.

The film Conclave has shown the world not only what to expect now — the runners and riders, the dinners, the sealed building — but also the battle lines. Pell’s j’accuse may well serve as a manifesto for the conservatives. “The first tasks of the new pope will be to restore normality, restore doctrinal clarity in faith and morals, restore a proper respect for the law,” he wrote. Or, as Scavizzi puts it in Conclave: “We do not need a church that will move with the world, but a church that will move the world.”

The liberals, meanwhile, have their reform arguments ready. “I don’t believe there’s a compelling theological reason why the Pope could not name a woman cardinal,” says the real-life Cardinal Joseph Tobin of New York. ”Homosexuality is not a sin,” says Cardinal Reinhard Marx (Munich and Freising). “The position of women in the church, a sexual morality that many may find incomprehensible to move forward here, is a prerequisite to gaining new momentum.” They are the outriders; behind them will be other cardinals wishing to push the church in this or that direction.

There is Cardinal Luis Antonio Tagle from the Philippines, often seen as an Asian version of Francis; a “global south” cleric of the people, keen on the church’s role as a “field hospital” and the need to get its hands dirtier. He is likely to be a stylistic successor to Francis while keeping the most problematic issues, on sex and gender, off the agenda.

The main conservative candidate is Hungary’s Cardinal Peter Erdo, a theologian who has spoken out against “ecclesiastical lawlessness”. He even spoke out about churches taking in refugees (as advocated by his Austrian counterpart) as it may aid and abet human trafficking. For this he was denounced as heartless but it was, I suspect, a plea for less superficial argument. The favourite compromise candidate is an Italian, Pietro Parolin, a Vatican diplomat seen to be a pragmatist. He’s also 72, and young cardinals do tend to like older popes.

The process and lack of openness make it all hugely unpredictable; very few of those who have bet (so far) $2.5 million on the next pope will be getting a serious return on their money. I wonder if the Vatican is likely to change very much, even if we’d want it to. Its dysfunction is such that it may be better being ineffective; going easy on reforming a church that isn’t, when all things are considered, doing too badly.

The pope’s main job, of course, is to represent the faith. Francis did that to the end: his last day was spent delivering the Easter blessing, in spite of his visible frailty. A friend of mine was in St Peter’s Square and caught a glimpse of him, going into the crowds when he barely had the energy to lift his hand to wave. His methods were controversial, his theology contested, but few could doubt his faith. And that, in the end, is what the church needs most.