Not Religion Per Se
When you're trying to select a candidate for a position, determining whether the person is academically qualified for the job is comparatively easy. You have things like education and work history which you can evaluate qualitatively.
What's difficult about the hiring process is identifying some of the more difficult-to-quantify attributes of the candidate. Which is to say, are their individual eccentricities going to be compatible with the team they're going to be working with?
If one were applying for a teaching position in a Catholic school, and one were Protestant, it might be wise to add that to the CV simply to avoid wasting time or getting into unpleasant conflicts down the road. If I were reviewing the application, I might consider it a thoughtful addition.
On the other hand, volunteering information which is personal, and irrelevant to a particular occupation (e.g.: religion, marital status, Macintosh user ;-)) can sometimes be an indication that the applicant has a chip on his shoulder or a neurotic sense of entitlement. Nobody wants to come to work and deal with the daily ramblings of a drama generator.