I hadn't heard of Catholics Anonymous, but

I know there's a Fundamentalists Anonymous.

You seem to contradict yourself when you say,

"In your mind, try your best to separate 'the faith' from 'the institution.' Without the institution, the faith could not survive, and without the faith, the institution could not survive."

If both parts of the second sentence are true, I don't see how you could separate them. But dissidents of many faiths argue otherwise: that the instition needs the faith, but not vice versa.