A few different thoughts have been coming together to prompt this post. The first one was the reaction of the people present at a recent public meeting about faith schools. There were a lot of criticisms - including suggestions of indoctrination - and a show of hands revealed quite a few people against any faith involvement in schooling.
In one sense, that was surprising, as we have a good local primary schools with a church foundation, as well as popular church high schools. However, I have also seen the concern and negative feeling about churches having any involvement in running institutions when a secular college was merged with a church one to form the University of Cumbria. The perception of the church as homophobic, sexist and bigoted runs deep. Furthermore, people question whether the state should support faith at all. In 2005, a Guardian/ICM poll recorded 64% opposing any government funding of faith schools.
Historically, the church was the first agency to provide schooling in England and many of the schools we now have in the state-sector are the legacy from the parochial schools which pre-date universal state provision. I suppose one could argue that if the church started schools and Universities in this country, it's a bit churlish to evict them them now.
I think there are several issues with faith and education. Firstly, is it indoctrination? Well, a school might have a very clear agenda to propagate a faith; others might have a "Christian ethos" (often vaguely defined) with no particular agenda. I have to say that if they are indoctrinating children, the net result seems to be pretty unsuccessful. In fact they often have the opposite effect, with overdoses of religion immunising people from faith later in life. For instance, my secondary school gave us daily assemblies, 3 of them were for the whole school with reading, hymn and talk. Of about 800, only a tiny handful ever met at Christian Union, and assemblies and RE lessons did nothing to help it sustain its activities.
Secondly, do they generate sectarianism? That's a harder question to answer. I haven't come across any militant Anglicans produced by Church of England schools. [Wonder what they would do? Guerilla jumble sales? Aggressively enlist people for evensong?] However in Northern Ireland people may answer that question rather differently. I remember students at St Martin's College, Lancaster who came from Belfast saying College was the first place they had ever got to know people from the other side of the divide, as their previous education was in a purely Protestant or Catholic environment. In the English context, I understand that C of E and Catholic state schools may not discriminate against people of other faiths in staff recruitment, except for RE teachers, and there are often non-Catholic or non Anglican Christians as well as other faiths, agnostic and even atheist teachers in such schools. That makes indoctrination rather difficult to achieve.
The third question is whether it's possible to provide a 'neutral' education. Suppose schools had a policy of no exploration of the idea of spirituality at all, which is what I presume some would want. That's a belief standpoint. By taking the possibility of the spiritual out of the education system, you have already adopted a stance, just as much as you would in a faith school. It seems to me the real question is how open and free pupils are to question and to explore ideas which are not the 'given' in the school they attend.
The important question behind all of this is whether any state resources should, in any sense, be invested in what atheist critics would regard as the propagation of religion. I can see the case that in a genuinely secular state that they should not (although faith groups often sustain community and charitable activity that augments state provision, so charitable status for tax, etc could be argued for even in a secular state). The difference in the UK is that we are not a secular state. We have an established church, the monarch is the supreme governor of the Church of England, we have Bishops on the House of Lords. The other side of that coin is that Parliament has a say over church matters (it had to approve the ordination of women, approves parochial fees, and the Commons threw out a revised Church of England Prayer Book in 1927 & 1928)
Perhaps some of the current proposed reforms may start to change that. I would certainly favour an elected upper house, provided it was elected by a genuinely proportional system such as Single Transferable Vote. However, if Parliament no longer provides a voice for the Church of England, then it ought to be time for the Church to be able to govern itself without reference to Parliament.
There is a perfectly logical case for the state becoming secular, but to achieve that aim is far from simple. There's plenty more to debate.