England's state religion is an accident sustained by apathy: lacking any logical existence at the heart of the nation, it survives because it is already there. No one would campaign to create an official Church of England, if we had not inherited one; other parts of the country do without it. Non-believers, when they think of the English church at all, tend to see a benign relic, the keeper of country churchyards, a modest, often helpful and mostly inoffensive part of the national fabric. Its rituals involve a declining number of citizens and its tortured internal politics are a mystery, but it is still an important – and often profound – part of many English lives. The fact that the monarch is also its supreme governor, that some of its bishops sit in parliament, and that its senior clerics are appointed by the prime minister is both indefensible and profoundly unexciting.

This tolerant indulgence, though, is being strained. The Church of England now expects both the benefits of establishment and the cultural freedom of private religion. At the very least, a national church should not become disconnected from the best values of the country it serves. But as the general synod, which begins tonight, will again confirm, the Church of England is strangely unwilling to do this. It devotes a shocking amount of energy to debating the supposed inferiority of women, gay men and lesbians. These issues matter intensely to some believers inside the church, but they make it look intolerant to the much larger number of people outside it.

The church's position on these issues is now out of line with both the law and the mood of the times. Rowan Williams, whose support for the established church flowered only after he became the archbishop of Canterbury, once noted: "We have a special relationship with the cultural life of our country and we must not fall out of step with it if we are not to become absurd and incredible." He said it. But the truth is that his church fell out of step long ago.

This week a gay but celibate cleric, Jeffrey John, the dean of St Albans and a man of the highest intellectual and moral standing, was rejected as a candidate for the diocese of Southwark because of his sexuality. No other private or state institution would have been allowed to do this. No institution, either, would be allowed to bar women from applying for the job, allowing them to be ordained but not promoted.

The internal agonies of a church caught between its Protestant and Catholic, and its liberal and conservative, tendencies cannot excuse this official institutionalisation of intolerance. It is true that disestablishing the church would require a huge amount of constitutional unpicking – much of it beneficial, such as the removal of anti-Catholic discrimination from the Act of Settlement. No government is likely to devote parliamentary time to the cause. It is true, too, that the established part of the church tends to be the more liberal, and that pulling back state involvement may do little to advance the cause of men such as Jeffrey John. Any mechanism that allows dialogue and change between the hard core of the committed and the penumbra of the vaguely supportive has something to be said for it. Religions that are entirely cut off from the surrounding culture neither die nor fade away, but turn crazy and dangerous. But formal disestablishment need not mean isolation, only the end of an unhealthy pretence that one church above all others can speak for a diverse nation.

David Hume once argued: "The union of the civil and ecclesiastical power ... prevents those gross impostures and bigoted persecutions which in all false religions are the chief foundation of clerical authority." The Church of England can obey his advice and accept the tolerant norms of modern society, as defined by the state. Or it can decide, privately, what it believes. Caught between the two, it risks becoming, as its archbishop feared, absurd