There can be little rest this Christmas for literalists who have just seen off the Church of England's attempt to defy the women-suppressing message of the scriptures. In his new Jesus of Nazareth: The Infancy Narratives, a prequel to two other books about the Saviour, Pope Benedict XVI establishes that the role of donkeys is also subject to wilful over-representation by many modern Christians, who persist in honouring them in Nativity scenes. The star and shepherds, a multitude of the heavenly host and a stable – all these, he finds, are plausible. "In the area round Bethlehem, rocky caves had been used as stables since ancient times." But the manger does not indicate the presence of donkeys, cows, sheep or any livestock whatsoever. "In the Gospel, there is no reference to animals at this point."

If the Pope is inclined to forgive fanciful iconography in this respect, "no representation of the crib is complete without the ox and the ass", we can surely expect something more from the punctilious Anglican laity. Having now witnessed their fervour, one pictures these purists, come Christmas, scanning parish churches for evidence of the donkey heresy and either confiscating the farm animals or, like their predecessors in the Reformation, vandalising the sentimental ornaments or smiting their heads off. As his holiness says: "With a text like the Bible, whose ultimate and fundamental author, according to our faith, is God himself, the question regarding the here and now of things past is undeniably included in the task of exegesis."

Donkey-wise, the inevitable result can only upset observers who feel like David Cameron, in the most striking of the many vehement, post-vote rebukes by church outsiders, that it is time for the church to chill and "get with the programme" – with that statement's unspoken corollary "or else". It remains to be seen which particular sex equality programme Cameron would most like the church to get with: positive discrimination or the highly effective, notional kind favoured by his own party, FTSE companies and the BBC, whereby qualified women are theoretically entitled to the highest office yet in practice invariably denied it.

If only the Anglican laity had gone for the second type, usefully demonstrated by Lord Patten's latest BBC appointment, they too could have saved their church from the sort of punishing public inspection that now threatens centuries of comfortable accommodation and fudging. For years, non-worshippers, even progressive ones, have been soothed into quiescence by John Betjeman and The Vicar of Dibley.

As recently as July, when Nick Clegg presented plans for a reformed upper chamber, he was content to reserve 12 places for bishops, regardless of their marginal claims to any mandate, their presumption of supernatural authority and the expectation, reestablished this week, that each of the qualified candidates would have a penis. Now, following one of history's most spectacular examples of biting off nose to spite face, congregants who could, after all, have escaped into any number of woman-free Christian outfits, have, in order to preserve their faith's antique, discriminatory practices, jeopardised its status as the established church. Giles Fraser calls it "suicidal". To sum up, as a secularist: rejoice.

If it is much too early to predict the last ever daily service or Anne Atkins Thought or, equally, the end of prayers for Prince Harry at choral evensong, opponents of an established church will surely want to celebrate last week's vote as a development to rival the ruptures of the Oxford Movement or, more recently, the defrocking of the rector of Stiffkey.

True, the vote on women bishops was an insult to its more enlightened members, whose spiritual practices will interest outsiders so long as bishops enjoy temporal power. Before it flopped, to the outrage of Maria Miller and David Cameron, I, too, would have supported what the outgoing archbishop, Rowan Williams, has called "rectifying the anomaly" since that anomaly inevitably touches, by excluding women, upon the church's political activities. It's natural to sympathise when this obviously well-intentioned person says the church has "lost a measure of credibility". On the other hand, supposing female bishops really constitutes some sort of advance, does one want the church to have any more credibility than it has already?

A victory would only, as Williams now confirms, have entrenched his church's claims to worldly authority – and with that, the ambitions of Britain's rival faiths for enhanced, equal-opportunity meddling. Only because of the media access conferred on Anglicans by virtue of their political privileges is it now routine to hear contributions from an array of Catholic, Jewish, Hindu, Sikh and Muslim professional clergy, their religions also exempt from the equality laws and compared with whom the Anglican legislators occasionally can resemble a collective of radical feminists.

"Their presence in the Lords is an extension of their general vocation as bishops to preach God's word and to lead people in prayer," explains the church. Of course, it does not stop with preaching. Each time one of these men substitutes supernatural authority for argument he validates the conviction of pious MPs, of all faiths, that their personal religious prejudices should be allowed to restrict the behaviour of non co-religionists on everything from abortion and blasphemy to marriage, assisted dying and infertility treatment. The less credibility for any of this the better.

So it is devoutly to be wished that Mr Cameron's proposed corrective, a "sharp prod", barely registers in the padded hindquarters of Bishop Welby's church. Rather, one hopes, all the epiphanies will continue to be on Mr Cameron's side, as he realises with what must be growing dismay that the kindly old religion that educates, at the state's expense, his own children and roughly one million others is still far from embracing his own ideals on diversity.

Even if it never dawned on Mr Cameron during the long period of bi-monthly church attendance that will have been required from this previously infrequent congregant if he wanted to snag a precious "foundation place" at his children's school, it must now be clear that an institution so unwilling to conform with equal opportunities law must be as undesirable in state education as it is inside the legislature.

Leave aside, for now, the views of this and other providers of faith-based education on, say, gays, evolution, polygamy, hell, sex before marriage, Salman Rushdie, physical chastisement, Satan, apostasy, Noah's Ark, original sin, adultery, paradise and literal transubstantiation, and simply the fact that women are officially inferior within so many of these influential bodies should be enough, like the Anglican vote, to make the prime minister "very sad". More than very sad, in fact, since their victims are young enough to brainwash.

If the Church of England deserves a "sharp prod" for its backwardness, what is the appropriate punishment for a government whose next batch of free schools will be one-third religious, including a proposal from creationists? A plague of frogs?