Hmm. It's been a long time since I've looked at my birth certificate. I was baptised at the hospital by a prominent national figure in the church who was passing through and looked at some sort of information for persons of my mother's denomination.
It is POSSIBLE that he went door to door around the ward asking the mothers their religion, but I think he looked over something else. He wasn't called there by my family, I know that.
I can remember being asked my religion on admission to the hospital and having it on my wristband. Once, when I went in for an unbelievably minor procedure (that these days is done totally on an outpatient basis), someone even came in the room and asked if I had been seen by the rabbi.
You’re right, they know an awful lot about us, but I am not sure it is from the birth cert.