The news that parents are still scrabbling to secure primary-school places for their children fills me with profound sympathy. Well, no, that's not exactly true. What it actually fills me with is profound relief that my own daughter is due to attend the lovely Church of England state primary across the road in September. But my relief – all right, my smugness – is mingled with my guilt over how my partner and I nabbed that precious school place. Yes, you guessed it. We had our daughter baptised. Even though I'm an atheist of the Dawkins-for-prime-minister variety, I promised to renounce the devil and steer my daughter towards the pearly gates.

It was an infuriating decision. The school is so close to our house that if I lobbed my copy of God Is Not Great out of the bedroom window it would land in the playground. But in the school's "oversubscription criteria", proximity lies in a lowly sixth place. Above it, in descending order, are being in care, going to the parish church, being a practising Anglican, being a practising Christian, and being a baptised Christian.

It is a mind-boggling, somewhat sinister list to read. And it doesn't seem to have much to do with what church schools were set up for, back when there was no such thing as a comprehensive system, and when pretty much everyone in England identified themselves as Anglican. In the 21st century, when we have taxes rather than tithes to pay for education, and when a quarter of us tick the "No religion" box on the census form, it's strange that we haven't scrubbed something as divisive as theology from school admission policies. Just think of the social-cohesion benefits that might follow. Instead of instructing our youngest and most impressionable citizens to separate themselves along religious lines, we could be spending five days a week teaching them what they have in common.