Especially if the surveys include self-report questions. I have been a life-long atheist. But it is only the past 15 years or so that I have voluntarily identified myself as such. It is only since 2001 that I have openly advocated as a militant atheist. (Thank you, 9/11 and Bush's and Republican overt religiosity.)
Self-report data always has these problems. The only way to do it right is to have multiple questions which can triangulate on the answers in the public such that the self-report bias is factored out.
I am not a psychological researcher, so I have no expertease in the vagaries of this stuff.
If you want a source, I invite you to tune into the Reasonable Doubts podcast, which has a regular segment entitled, God thinks like you which delves into precisely these questions from a analytical viewpoint, Done by a PhD psychologist who specializes in just these questions. You will learn loads and loads from "Doctor, Professor Luke", as the call him.
Sorry that I cannot help further, but if you haven't listened to Reasonable Doubts before, you may be in for a real surprise. It's my favorite non-believer podcast because all it talks about is religion. And a non-believer has to be educated about religion if he/she is to make a difference. BTW, all the RD hosts are non-believers.
Another of my favorites is The Bible Geek, Robert M. Price. He's a bit of a curmudgeon and more than a bit controversial. But he is has a compendious memory for the bible and is also a non-believing former evangelical. Fun stuff because he doesn't take himself too seriously. But the discussions are very, very deep.
Just thought I'd help. I know you'll like Reasonable Doubts. (The Bible Geek is even interviewed on one of the RD podcasts.)
Relax and enjoy, as Douglas Adams might have wrote.