Your hypothesis regarding parents certainly merits further consideration and analysis. You would have to bring in the rebellious teen years where all things the parents put forth are rejected. There are many children who grow up without parental influence who believe in God. I think there are a lot of issues involved in it rather just one.

From personal experience, I can tell you that I was not really pushed one way or the other; my parents did not go to Church but they did drop us off if we indicated we wanted to go. I just don't remember them ever encouraging or discouraging it one way or the other. I only half-assed believed in God and paid no attention to any of it until one evening as I was driving down the road and I had a very sudden very personal mystical experience and I immediately committed myself to God. That was outside the realm of parental influence or religious influence but something that happened to me personally. Many people have this same type of sudden event.