One of the best schools local to me is a CofE school. It has a relatively large catchment area, and spreads across several villages, where the population isn't particularly diverse.
Allocation based on faith is 4th on the list, with resident in catchment, sibling priority, looked after children being 1st, 2nd and 3rd. In reality the majority of places are allocated children in the first three categories.
I attend the church which is attached to this school - its actually the closest church to us, but we are not within catchment for the school. Our vicar is very wise to the concept of "on your knees to save on fees" and rightly so.
There's a Catholic school also in our town, and again, allocation of places is the same as above. Because of the location of the school, this is a very ethnically diverse school (town vs rural village)
The school we are in catchment for, is dreadful both in terms of attainment and behaviour issues, so will we apply to an oversubscribed CofE school which aligns with our faith over a mega-school with issues? Absolutely.