My guess is that many people think the point of state religion is something like the following. If we have a society in which the majority of the population has strong religious commitments and places great trust in religious leaders, then if the secular authorities act in some way that the religious authorities oppose, the priests and monks may denounce the secular authorities and the wider population may be forced to choose between their souls and obedience to the law. This could be a recipe for unrest. In such circumstances, it may be a reflection of pragmatic reality that one includes the religious authorities in secular decision-making.
If this were indeed the reason for including religion in state business, then in a society in which most people did not have strong religious commitments and/or in which respect for religious leaders were low, this rationale for state religion would be gone. Maintaining an official state religion would be pointless - better to consult with the Bob Geldofs and other respected public figures that would actually carry some weight with the masses.
But this is not why I believe in having a state religion.
The main function of state religion is not as a kind of quasi-democracy via priests. Rather, its main function is to provide a spiritual and moral framework within which policy-making is set. This is even more important in a society in which there is great moral and religious diversity, for without us having an official position, there would be no way to anticipate the evolution of the moral and spiritual framework of policy over time. There would be no official enduring Position of the Establishment, against which the momentary developments in policy could be understood. We would not know how radical or reactionary particular policies were, without some underlying sense of the Background.
And this matters. As David Willetts pointed out in an interesting speech in February this year, without some guiding principles, there is a "multiple equilibrium" problem in public policy. For example, we might all choose to drive on the right hand side of the road; we might all choose to drive on the left; or we might randomly decide before each journey on which side of the road we would drive. Without some principle to guide us, it would be very difficult to anticipate whether a policy decision over which side of the road we should drive on would result in right-hand driving or left-hand driving. So if we were manufacturing cars in advance of the decision there is a good chance we would build the wrong sort of car.
This problem runs very broad. It would be very difficult, without some sense of the underlying moral and spiritual assumptions of the Establishment, to anticipate the attitude of policy towards women, immigrants, embryos, tax avoiders, those that have built up unsustainable debts, those that receive unearned income, those that make money from the death or ill health of others, or many other issues to which moral and spiritual attitudes are important.
By having an Established religion, we temper the effects of democracy in important ways. Our Established religion is reflected in the checks and balances of our constitution: in the monarchy, in the Upper Chamber, in the judiciary, in the organic traditions that our Establishment embodies. We could not hope not to have a society in which moral and spiritual assumptions for an Establishment were entirely absent. All that could happen is for us to replace the Anglican Establishment with some other moral and spiritual framework. Some alternatives would not be too bad. Personally, if we are not to have Anglicanism, I would propose the use of Sunni Islam. I don't see that it matters much that most of the population are not Sunnis. With Sunni Islam as our established religion, we would have a pattern for the Establishment that had been proven, at other times and places, to be compatible with a liberal and tolerant society.
An alternative might be to have the moral and spiritual assumptions of one of the least numerically significant religions in our society: Materialist Atheism. This is unfortunately a highly intolerant religion, and has proven, where Established, to result in very grim societies. It also offers little clear guidance, or in fact answers that many people simply reject, upon too many moral and spiritual issues (its "there is no answer" answer somehow does not satisfy). And of course, the argument that there would be something more "democratic" about having Materialist Atheism as our established religion would be absurd, for the number of Materialist Atheists is tiny. This would be every bit as much a religion of the elite as Anglicanism or Sunni Islam.
If we really wanted the majority religion, it would be (as it is in all societies, once one scratches beneath the surface) Animism. But Animism is such a chaotic framework, and the morals it propounds so individualistic, diverse, and unstable, that it is almost a definitive feature of civilisation that one employs something other than Animism (imagine how it would be if we understood our country's moral and spiritual framework as defined by belief in ghosts or astrological signs or messages from Presences at special places, the output of healing crystals and ouija boards, or the results of taboos and practices such as touching wood for good luck).
Anglican Christianity provides an excellent system for a state religion in a tolerant and independent state. It is a religion predicated upon catholicism - the technical term for being "broad church" - and is the most successful "highest common denominator" broad church in the world. Its framework is thus well suited to a tolerant and broad society. It provides clear moral and spiritual positions, unlike the chaos of Animism. It does not require of its leaders commitment to foreign powers or internationalism, and thus is superior to the Roman Catholic religion for an independent state such as Britain. Anglicanism is an evolving religion with a commitment to Truth. It is philosophically sophisticated, offers answers to most existing questions and has formulae for providing new answers to new questions as they arise (e.g. it will offer us attitudes to artificial intelligences or to aliens when the time comes).
With Anglicanism as our official religion, we can anticipate the attitude of the Establishment, and interpret current policy versus that underlying scheme, allowing us to guess whether policy is more likely to revert to past positions from current trends or to continue along its present path. Our political leadership is forced to confront moral censure and challenge from officially designated sources. This improves policy, taking it beyond the considerations of the moment to longer-term and higher things.
As I say, Anglicanism is not the only possible candidate - Sunni Islam is the obvious alternative. But Anglicanism would do the job well, if Anglican leaders took on their task with proper vigour. Removing our Established religion would be a major structural blow to our already diminished constitution and our already enfeebled Establishment. We should be seeking ways to strengthen and grow our organic constitution, not further ill-conceived and uncomprehending ways to vandalise it.