The pope's offer to Church of England members to switch to the Vatican was ill thought-out and could signal a struggle for the soul of both churches

Over the centuries, the great church councils of Christian history have normally been held in magnificent echoing basilicas and stately palaces – but the church moves with the times. In 2003 a luxury hotel in Dallas, self-proclaimed as the largest in Texas (now that's big), hosted a gathering of very angry conservative American Anglicans, determined to do something about the consecration of a gay man, Gene Robinson, as a bishop of the US Episcopal church, sister church to the Church of England.

As they dithered about what doing something might mean, the delegates were electrified to receive an encouraging message from no less a figure than Cardinal Joseph Ratzinger. This was remarkable, because Ratzinger was head of the Roman Catholic church's Congregation for the Doctrine of the Faith: what in less mealy-mouthed times was known as the Inquisition.

Rather than ordering this roomful of Protestants to be burnt at the stake, Ratzinger assured them of his "heartfelt prayers" for all those taking part in this convocation. "The significance of your meeting is sensed far beyond [Dallas] and even in this city, from which St Augustine of Canterbury was sent to confirm and strengthen the preaching of Christ's Gospel in England." There was wild applause.

So the former Cardinal Ratzinger, now Pope Benedict XVI, has form when it comes to sudden dramatic interventions in Anglican affairs. And now he has done it again. The announcement that whole parishes or even dioceses of Anglicans will be welcomed to Rome and allowed to keep many of their customs has been channelled through his successor in that line of prelates heading the Inquisition, Cardinal William Joseph Levada.

Benedict's idiosyncratic version of ecumenism overturns all the careful negotiations between the mainstream churches built up over the past half century. Rather, as in various other controversial personal initiatives of his pontificate, to do with Muslims or condoms in Africa, the pope has jumped into a delicate situation regardless of consultation with those in the Vatican who have charge of such matters. Senior figures in the Catholic church in England did not all seem up to speed with the decision when it was announced.

There has been a great deal of excited talk about this move: one hysterical front-page headline in the Times proclaimed that 400,000 Anglicans were poised to head for the Tiber. This turns out to be the self-estimated membership of a faction calling itself the Traditional Anglican Communion.

Equally extravagant claims that this could be the end of the Protestant Reformation need to be taken with several fontfuls of salt. It is in the interests of various discontented groups on the margins of Anglicanism to talk up the significance of the latest piece of papal theatre, while ignoring its wider context.

This much broader struggle within Christianity at first sight appears to be about sex. Throughout the world, the most easily heard tone in religion (not just Christianity) is of a generally angry conservatism. Why? I hazard that the anger centres on a profound shift in gender roles traditionally given a religious significance and validated by religious traditions.

The conservative backlash embodies the hurt of heterosexual men (or those who would like to pass for being heterosexual men) at cultural shifts which have generally threatened to marginalise them and deprive them of dignity, hegemony or even much usefulness. What they notice amid their hurt is that the sacred texts generally back them in their assumptions, and they therefore assert the authority of sacred scripture.

They fail to hear other voices in scripture, just as two centuries ago those who perfectly rightly believed the Bible legitimised slavery failed to hear the Bible's other message – that freedom is a universal Christian value. Self-styled "traditionalist" Anglicans and the Curia both emphasise ancient authority in their efforts to outface the inexorable realities of modern life, which some others might style new workings of the Holy Spirit. King Canute's courtiers would have signed up to Pope Benedict's proposed new jurisdictions.

The other concealed struggle behind this move is an internal split within the Catholic church over the legacy of the Second Vatican Council, that half-completed church revolution in the 1960s and 1970s, which suddenly introduced to astonished Catholics religious customs previously enjoyed only by Protestants, such as worship in vernacular languages, popular music in the liturgy, layfolk involved in church government and the faithful thinking seriously for themselves on matters of doctrine and biblical interpretation.

Virtually no one in the Vatican dares openly criticise the great council, but neither John Paul II nor his successor have been enthusiasts for the messages embodied in its statements of faith, which so brusquely overturned the safe doctrinal texts prepared for the council by the Holy Office (the Roman Inquisition).

They have been horrified by many of the council's results. Since John Paul II's election as Pope in 1978, there have been grim attempts to suppress growing Catholic calls for married clergy, for women clergy, for a greater real place for the laity in church decision-making, even merely for a real say for bishops of the church in decision-making.

John Paul II and Benedict have created the most centralised regime that Catholicism has ever known – a far cry from its state in either the medieval period or the Counter-Reformation. It is with an anxious ear for those alternative voices, not much different from those of mainstream wishy-washy liberal Anglicans, that Pope Benedict seeks to encourage those who think like him beyond the walls, and to bring them inside the fortifications.

Much is left unsaid amid the present triumphalist crowings of those Catholics who see this as a victory over a feeble, tottering Anglicanism, since Anglicans are temperamentally disinclined to blow their own trumpets. The Church of England is not about to disintegrate, as anyone who knows its day-to-day life, rather than listening to what journalists say about it, will be aware. Most Anglo-Catholics and evangelicals are fed up with all the name-calling, intolerance and calls for revolt.

The flow of Roman Catholics to Anglicanism has its counterpart in the flow of dissidents in the other direction. One particular flow has been little commented on: in the 1990s a few hundred Anglican clergy took a generous compensation package from the C of E and were received into the Church of Rome. A significant number then came back to Canterbury, because Rome was not what they expected.

It will be interesting to see exactly which customs the Vatican is going to allow from the past rich five centuries of Anglican worship, life and thought. Married clergy will have to be part of the package. What do faithful celibate priests of the Roman Obedience think about seeing their new colleagues happily allowed to bypass compulsory celibacy?

This will be different from the so-called "Greek Catholic" churches in eastern Europe. For centuries Greek Catholics have accepted Roman authority alongside married clergy with Orthodox beards and Orthodox liturgy, but they have had the decency to keep themselves to themselves.

These newly acquired Anglicans will be much closer to the centre, much more annoyingly able to go their own way in the midst of ordinary Catholic parishes.

There is one killer fact about the pope's present move. "Traditionalist" Anglicanism is a shotgun marriage between incompatible groups: extreme Anglo-Catholics and extreme evangelicals. One group believes an Anglican holy communion is the mass, and surrounds it with appropriate magnificence and ancient ceremony; the other thinks the mass is a blasphemy and stresses that holy communion is the Lord's supper, plain and simple.

Because of that, they cannot even agree on what a clergyman is, or what he does (though they can all agree that he ought to be he). Evangelical traditionalists, meanwhile, have no time for a reunion with an unreformed Church of Rome. Their alliance with the traditionalist Anglo-Catholics has been one of convenience, because both sides cannot stomach women in positions of clerical authority (for entirely opposite reasons) and hate the idea that homosexuals might be just part of the spectrum of boring normality in God's creation. (Anglo-Catholics are more muffled in their outrage on this one, given how many of them are gay themselves.) So the pope's move will split the traditionalists down the middle and reveal how fragile their alliance is. The best law in church history is the law of unintended consequences.

In one sense, this is a storm in a teacup, stirred by an elderly cleric in the Vatican with a private agenda and a track record of ill-thought-out policy moves. In another, it is a fascinating moment in a confrontation as much a struggle for the soul of the Church of Rome as of the Church of England. Once we have got past the screaming headlines, we should keep an eye open for the real story.

Diarmaid MacCulloch is professor of the history of the church at Oxford University. His latest book is A History of Christianity (Allen Lane), and his BBC4 television series on the same subject begins on 5 November