I went to a Catholic school in the 90s, and it was genuinely the case that people would think you were a bit weird if you said you believed in God. I remember a not insignificant number of people using the mock GCSE RE exam as an excuse to take the piss.
When the stuff came out about the Catholic church, it was genuinely amazing to me that there was never even a discussion of banning them from running things like schools. I honestly think if it was a charitable organisation rather than a church, all of the schools would have been taken into local authority control.