I'm a little bemused about the religious schools in state sector hoo-har also.
My children both attend(ed) a C of E primary.
All that happens is that they get a good cultural grounding in the traditional British faith, as well as an utterly positive and sensitive grounding in other faiths.
I am an unbeliever (so are they). But I don't at all see why unbelief should necessitate an abstraction from a central cultural feature of our society.
The Church is a cultural enterprise, like theatre, sport, and so on. Our society is being ravaged by valuelessness. In the absence of traditional, culturally entrenched values we don't all suddenly become perfectly rational and moral. We are denuded and prey to a nihilistic consumerism.
We need to give our children a rich common culture. That is very far from amounting to religious indoctrination, which state schools shouldn't (and largely don't) engage in.