After a full year in office it ought to be fairly clear what kind of pope the new man in the Vatican is turning out to be. Yet if you survey the raft of commentaries on the first 12 months of Pope Francis, which have appeared all around the world in recent days, you discover a surprising lack of agreement. A battle is underway for the soul of the pope.

All the verdicts share a standard litany of anecdotes. He is the pontiff who lives in a hostel, carries his own bags, is driven round in an old Ford Focus, and makes unexpected phone calls to strangers that open: "Ciao, sono Papa Francesco." He is a priest who practises what he preaches: he embraces the disfigured; invites the homeless for breakfast; suspends bishops with opulent or self-regarding lifestyles; and follows a regimen of ostentatious frugality.

But is there anything more to this shift in papal style than a cosmetic rebranding of a global corporation that has undergone massive reputational damage in recent decades?

There is a carefully cultivated ambiguity about the man who is the 266th successor to St Peter. And it is producing a war of words between conservatives and liberals, inside and outside the Catholic church, with each trying to claim the pontiff for their side in a religious culture war. The stakes are high. This is a pope who has attracted almost seven million visitors to papal events in the 12 months since he took office – triple the number who turned out to see Benedict XVI the year before.

A glance at his Wikipedia page reveals one side of the battleline. It has clearly been written primarily by religious conservatives. Its entries seek predominantly to accentuate the religious orthodoxy of the man who was born Jorge Mario Bergoglio. Throughout his papacy, it insists, Pope Francis has been a vocal opponent of abortion. He has asserted that he is a "son of the church" and, therefore, loyal to existing doctrine. He has maintained that divorced and remarried Catholics may not receive holy communion (a totemic issue in the traditionalist v progressive divide). The reason he does not sing Gregorian chant during mass is because he had part of one lung removed as a young man.

The casual reader would be advised to take all that as a large dose of spin. Francis's opposition to abortion has hardly been vocal; indeed, he has proclaimed that the church has hitherto "obsessed" too much about it. There is an artful inscrutability to what he means by "a son of the church"; it is a statement about the past, not the future. He has repeatedly hinted that he wants to end the policy of banning divorced and remarried Catholics from communion. He does not chant in Latin because he feels traditional styles of worship do not connect with ordinary people in the wider non-European world.

But what about the other side of the argument? Liberal Catholics, like the new pope's many enthusiasts in the secular world, look to the first non-European bishop of Rome for 1,200 years and see something altogether different. He is "a miracle of humility in an age of vanity", to quote Elton John. He has shown his readiness to break with tradition by washing the feet of women and Muslims. He has told atheists they can get to heaven so long as they "obey their conscience". Most onlookers are attracted by his demand for "a poor church, for the poor" and his letter scolding the rich and powerful at Davos for neglecting the "frail, weak and vulnerable".

Pope Francis kissing the feet of a young offender during a mass at the church of the Casal del Marmo youth prison on the outskirts of Rome in 2013. Photograph: AFP

The world was taken aback when the head of a church whose key document on the pastoral care of gay Christians is called Homosexualitatis Problema asked: "Who am I to judge?" Yet he has shown no such reticence in adjudging the shortcomings of the medieval monarchy that is the Vatican, describing its courtly Curia (officials) as the "leprosy of the papacy".

All of which, conservatives counter, is a wish-fulfilment Fantasy Francis. It mistakes style for substance and ignores the fact that the new pope's actual teaching demonstrates what the prominent US conservative George Weigel, a biographer and confidante of John Paul II, has called a "seamless continuity" with the German and Polish popes who preceded him.

So where does the truth lie? Is Francis a conservative or a liberal? Three areas offer pointers: politics, sex and governance, on each of which there are separate and distinct axes within the world's 1.2 billion Roman Catholics.

Politically, ever since 1891 and Pope Leo XIII's Rerum Novarum, the church has routinely excoriated the excesses of unregulated capitalism and sought to find a third way between it and what it feared as atheistic communism. Francis has been blasted by the US religious right for "pure Marxism" but Pope John Paul II said much the same thing in his day, condemning the "idolatry of the market" and arguing that Marxism was right in its identification of the "exploitation to which an inhuman capitalism subjected the proletariat since the beginning of industrial society".

Jorge Mario Bergoglio as a seminarian in Buenos Aires, Argentina, in 1966. Photograph: AP

What is different about Francis is that, where previous popes saw the issue as one of theological abstraction, his condemnations of capitalism come from living with its direct impact on the poor. After Argentina became the centre of the world's biggest debt default in 2001, almost half the population was plunged into poverty. "Not to share one's wealth with the poor is to steal from them," Francis proclaimed.

He has rehabilitated liberation theology. Rome sought in the 1970s and 80s to emasculate the movement, which grew up in South America and aimed to place the church on the side of the poor in struggles for justice and social change in the developing world. Bergoglio, as leader of the Jesuits in Argentina three decades ago, was part of the move to suppress it as a cover for Marxist class struggle. But as pope he has invited the father of the movement, Gustavo Gutierrez, to Rome and had the Vatican pronounce that liberation theology can no longer "remain in the shadows to which it has been relegated for some years". He has also asked another key figure, Leonardo Boff, who was once condemned to "obsequious silence" by Rome, to contribute his writings on eco-theology to a document Francis is planning on the environment.

It is on Catholic attitudes to sex that Pope Francis has been at his most ambiguous. The interview he gave to Corriere della Sera last week has only added to the opacity on contraception, divorce, homosexuality, gender and paedophile priests.

One of Francis's most innovative acts has been to issue an unprecedented questionnaire to discover what lay people around the world think of the church's handling of issues around sexual ethics. Early indications – from Germany and Ireland, to the Philippines and Japan – are of a seismic gap between official teaching and what ordinary Catholics believe and do. The exercise, ahead of two decision-making synods of bishops this and next year, has raised big expectations of change.

The pope appearing in a selfie taken by young pilgrims in St Peter's, Rome. Photograph: AP

But in Corriere della Sera, Francis praised Pope Paul VI's encyclical Humanae Vitae of 1968, which reaffirmed the church's longstanding ban on the use of artificial contraception. Pope Paul did this in the teeth of a major consultation with scientists, doctors and theologians who recommended lifting the ban. His decision undermined the credibility of the church in the eyes of many, if not most, Catholics. Last week, Francis said Pope Paul's "genius was prophetic, he had the courage to side against the majority, defend moral discipline, put a brake on the culture, oppose neo-Malthusianism, present and future" – though he added that the church should take care to apply its teaching against artificial birth control with "much mercy".

There was equivalence, too, in what he had to say on gay marriage. He reiterated the official line that marriage must be "between a man and a woman", but added that the church needed to "look at" the issue of civil unions to protect the civil and legal rights of "diverse situations of cohabitation". Then, in a classic Catholic one-step-forward-two-steps-back, Vatican officials insisted that in Italian "civil unions" refers to non-church weddings rather than same-sex ones.

And there was vagueness in another area where the pope will be judged by actions not words. "Women can and must be more present in the places of decision-making in the church," he told Corriere della Sera. What does that mean? He has previously said "the door is closed" on the ordination of women and he has ruled out female cardinals, saying "women in the church must be valued not clericalised". But it is unclear whether that is a deft deflection or an aspiration for change at a deeper level, since he clearly sees clericalism as a profound problem in Catholicism. He needs to appoint women to head Vatican departments – or create a council of lay advisers with women members to parallel his new Council of Cardinal Advisers – before anyone will take seriously his talk of "a more capillary and incisive feminine presence in the church".

But the most depressing aspect of the interview came with the pope's remarks on clerical sex abuse – his first since February's withering United Nations report denounced the Vatican for continuing to protect predator priests. Francis argued that most abuse takes place inside the family rather than in churches and added: "The Catholic church is perhaps the only public institution to have acted with transparency and responsibility. No one else has done more. And yet the church is the only one to be attacked." It felt as if the new pope was reading from Rome's same old script of myopic apologia and self-deception.

Transferring to Rome strategies he developed as archbishop of Buenos Aires has largely served Francis well. Yet in Argentina – although Bergoglio pursued a policy of zero tolerance for abusers and was scathing of the solution in the church in the US and Europe of just moving paedophile priests to a different parish – his policy was to deal with the matter internally. He did not call the police. The world has made it clear that is not acceptable. Dirty linen must be washed in public.

He may simply be buying time on these big issues. But there is a limit to how long he can pursue the strategy of one of his predecessors, John XXIII, who famously said: "I have to be pope both for those with their foot on the accelerator and those with their foot on the brake." Equal pressure on both results in getting nowhere.

Pope Francis addresses the Vatican Curia in December 2013. Photograph: Claudio Peri/ANSA pool

It is in the third area of disagreement within the church that it is clear Pope Francis, whether he is, at core, liberal or conservative, is most certainly a radical. For several centuries, the Vatican has acted as the master of the church around the world rather than its servant. Many in Rome hold firmly to that model. Francis wants that to change. It is in this area that transformation is proceeding with greatest speed.

He has sacked the cardinals running the Vatican Bank, brought in outside consultants who are closing dodgy accounts and set up a team to propose long-term structural reform. Management consultants are reviewing the Vatican's accounting, communications and management systems. He has set up a new finance department headed by an outsider, Cardinal George Pell, whose ruthlessness has earned him the nickname "Pell Pot" in his native Australia.

He has removed key conservatives from the body that appoints bishops. And he has set up the powerful Council of Cardinal Advisers from the world's five continents (all of them past critics of the Curia) to draw up a radical decentralisation of the papacy. He has instructed it to find more collegiate ways of decision making. Collegiality was the great upheaval advocated by the revolutionary Second Vatican Council in the 1960s but its vision was never implemented and was, indeed, undermined by the Vatican bureaucrats and popes who followed and who did not want to see doctrinal authority dispersed.

Many see the questionnaire of lay people and priests as the pilot for a new process of governance within the church that will inspire fresh and creative discussions by the Synod of Bishops, whose support staff has been doubled in Rome.

Certainly, the climate of conformity and fear that gripped Catholicism has lifted. Last month, Francis invited cardinals to debate the emblematic issue of communion for the remarried and chose Cardinal Walter Kasper, a liberal who has argued against the present ban, to address the meeting. When "intense discussion" followed, the pope declared himself delighted. "Fraternal and open confrontations foster the growth of theological and pastoral thought," he said. "I'm not afraid of this; on the contrary, I seek it."

To outsiders, that may sound like glacial progress, given the scale of the problems yet to be tackled. But within the Catholic church, it feels as if a revolution has begun. Pope Francis has done a lot in his first year. He still has much to do. But, at 77, he is an old man in a hurry.

• Pope Francis – Untying the Knots, by Paul Vallely, is published by Bloomsbury.

• This article was amended on 12 March 2014. The original stated "Liberal Catholics, such as the new Pope's many enthusiasts in the secular world ..." This has been corrected.