Someone who hates religion so much that their atheism has become a religion of its own.
Hank: "Man, it's so disgusting that our that our school has a bible study group! I'm going to make a petition to get an atheist club started!"
Bob: "You're totally a religious atheist."
Hank: "AM NOT! So do you want to come to the national prayer week protest blood drive on Saturday?"
The religious atheist believes that life needs constant examination and evaluation, that the moral ideals taught by great teachers of ethics need constant attention and personal affirmation.
He doesn't go to church or believe in any one thing, but he studies a lot of that stuff, kind of a religious atheist.