That Obama poster on the wall, promising hope and change, is looking a little faded now. The disappointments, whether over drone warfare or a botched rollout of healthcare reform, have left the world's liberals and progressives searching for a new pin-up to take the US president's place. As it happens, there's an obvious candidate: the head of an organisation those same liberals and progressives have long regarded as sexist, homophobic and, thanks to a series of child abuse scandals, chillingly cruel. The obvious new hero of the left is the pope.

Only installed in March, Pope Francis has already become a phenomenon. His is the most talked-about name on the internet in 2013, ranking ahead of "Obamacare" and "NSA". In fourth place comes Francis's Twitter handle, @Pontifex. In Italy, Francesco has fast become the most popular name for new baby boys. Rome reports a surge in tourist numbers, while church attendance is said to be up – both trends attributed to "the Francis effect".

His popularity is not hard to fathom. The stories of his personal modesty have become the stuff of instant legend. He carries his own suitcase. He refused the grandeur of the papal palace, preferring to live in a simple hostel. When presented with the traditional red shoes of the pontiff, he declined; instead he telephoned his 81-year-old cobbler in Buenos Aires and asked him to repair his old ones. On Thursday, Francis visited the Italian president – arriving in a blue Ford Focus, with not a blaring siren to be heard.

Some will dismiss these acts as mere gestures, even publicity stunts. But they convey a powerful message, one of almost elemental egalitarianism. He is in the business of scraping away the trappings, the edifice of Vatican wealth accreted over centuries, and returning the church to its core purpose, one Jesus himself might have recognised. He says he wants to preside over "a poor church, for the poor". It's not the institution that counts, it's the mission.

All this would warm the heart of even the most fervent atheist, except Francis has gone much further. It seems he wants to do more than simply stroke the brow of the weak. He is taking on the system that has made them weak and keeps them that way.

"My thoughts turn to all who are unemployed, often as a result of a self-centred mindset bent on profit at any cost," he tweeted in May. A day earlier he denounced as "slave labour" the conditions endured by Bangladeshi workers killed in a building collapse. In September he said that God wanted men and women to be at the heart of the world and yet we live in a global economic order that worships "an idol called money".

There is no denying the radicalism of this message, a frontal and sustained attack on what he calls "unbridled capitalism", with its "throwaway" attitude to everything from unwanted food to unwanted old people. His enemies have certainly not missed it. If a man is to be judged by his opponents, note that this week Sarah Palin denounced him as "kind of liberal" while the free-market Institute of Economic Affairs has lamented that this pope lacks the "sophisticated" approach to such matters of his predecessors. Meanwhile, an Italian prosecutor has warned that Francis's campaign against corruption could put him in the crosshairs of that country's second most powerful institution: the mafia.

As if this weren't enough to have Francis's 76-year-old face on the walls of the world's student bedrooms, he also seems set to lead a church campaign on the environment. He was photographed this week with anti-fracking activists, while his biographer, Paul Vallely, has revealed that the pope has made contact with Leonardo Boff, an eco-theologian previously shunned by Rome and sentenced to "obsequious silence" by the office formerly known as the "Inquisition". An encyclical on care for the planet is said to be on the way.

Many on the left will say that's all very welcome, but meaningless until the pope puts his own house in order. But here, too, the signs are encouraging. Or, more accurately, stunning. Recently, Francis told an interviewer the church had become "obsessed" with abortion, gay marriage and contraception. He no longer wanted the Catholic hierarchy to be preoccupied with "small-minded rules". Talking to reporters on a flight – an occurrence remarkable in itself – he said: "If a person is gay and seeks God and has good will, who am I to judge?" His latest move is to send the world's Catholics a questionnaire, seeking their attitude to those vexed questions of modern life. It's bound to reveal a flock whose practices are, shall we say, at variance with Catholic teaching. In politics, you'd say Francis was preparing the ground for reform.

Witness his reaction to a letter – sent to "His Holiness Francis, Vatican City" – from a single woman, pregnant by a married man who had since abandoned her. To her astonishment, the pope telephoned her directly and told her that if, as she feared, priests refused to baptise her baby, he would perform the ceremony himself. (Telephoning individuals who write to him is a Francis habit.) Now contrast that with the past Catholic approach to such "fallen women", dramatised so powerfully in the current film Philomena. He is replacing brutality with empathy.

Of course, he is not perfect. His record in Argentina during the era of dictatorship and "dirty war" is far from clean. "He started off as a strict authoritarian, reactionary figure," says Vallely. But, aged 50, Francis underwent a spiritual crisis from which, says his biographer, he emerged utterly transformed. He ditched the trappings of high church office, went into the slums and got his hands dirty.

Now inside the Vatican, he faces a different challenge – to face down the conservatives of the curia and lock in his reforms, so that they cannot be undone once he's gone. Given the guile of those courtiers, that's quite a task: he'll need all the support he can get.

Some will say the world's leftists and liberals shouldn't hanker for a pin-up, that the urge is infantile and bound to end in disappointment. But the need is human and hardly confined to the left: think of the Reagan and Thatcher posters that still adorn the metaphorical walls of conservatives, three decades on. The pope may have no army, no battalions or divisions, but he has a pulpit – and right now he is using it to be the world's loudest and clearest voice against the status quo. You don't have to be a believer to believe in that.

Twitter: @Freedland