"Should we have a national database of, say, religious beliefs? Almost instinctively the answer is no."

What about an ad system that can predict beliefs and home addresses? Ooops.

Google, Microsoft, Apple, every telecoms provider, every modern car maker..

It's definitely different to have a prediction than a database. Especially for something that can be denied like religious belief. If the nazis had such a db they would have killed much more efficiently I think.