‘Establishment’ is a way of recognising that we are still essentially a
Christian country, both in the sense that our history and culture have been
decisively shaped by the Christian faith and life and in the sense that at the
last census over 70% called themselves ‘Christian’. As the Archbishop said last
Monday, this means that the ‘established’ church has a special responsibility to
take thought for, and speak up for, the small minorities, and to ensure that
they are not squashed between an unthinking church and an uncaring secular
state. Hence his perfectly proper concern for the particular sensitivities of
Muslims, as indeed of Jews and others. And most Church of England leaders would
insist today that if some way could be found to share our ‘Established’ status
with our great sister churches, we would be delighted. But let’s not fool
ourselves. To give up ‘Establishment’ now would be to collude with that
secularism which postmodernity has cheerfully and rightly deconstructed. Rather,
the challenge ought to be to make it work for the benefit of the whole society.
To aim at that would be to work with the grain both of the Christian gospel
itself and of the deep roots of our own society and traditions.
Emphasis mine - this is a key challenge. Establishment, and the role of the church, is no longer a given in a secular society. In all sorts of ways the church is being asked to demonstrate competence, to compete for its place, and to demonstrate 'added value' (excuse me whilst I wash my keyboard out). In the education system, chaplaincies (NHS, prison, supermarkets), etc. the church is one provider among many, and the historical legacy of a privileged status is nearly spent up.
Another important factor is this: the New Testament is a document for people living out their faith in a society where other people hold the levers of power. Islam from the outset was a faith to run a country by (e.g. monotheism - gets rid of competing deities in a pagan society for the sake of national unity). In Judaism, the commandments and laws are an attempt to give some shape to the new Exodus community and turn them into a functioning society. Christianity has the ambivalent situation of inheriting the Old Testament (with a system of law, the Ten Commandments etc.), but being founded as an outsider group on the fringes of society. Where NT writings address church/state issues, it's normally to explore how Chrisitans should behave under persecution. The idea that they might one day hold the levers of power just doesn't seem to be entertained.
So on one level the church doesn't want to lose power and influence, because we hope to use that power and influence for good. But on another level we know that the church doesn't belong on the throne, and that our primary calling is not to run countries but to love God, love one another, and share Jesus. For some Christians and Christian organisations, that calling may express itself in politics, but for the church as a whole the relationship is more ambivalent.