It's been awhile, but most of the private schools I remember in PA were Catholic-affiliated. Here in Georgia, most of the really big churches are Baptist - there is one Catholic church near us but I'm not sure if they even have a school associated with the church. Most of the big Baptist churches don't seem to have big schools or a huge football program/presence. I seem to remember a private non-denominational school in Atlanta that might have had a pretty good football program going at one time - the name of the institution escapes me at the moment.
I think most people in Georgia choose a private school for education, primarily, rather than religious reasons. Our son did graduate from a private school, which our daughter did attend until she decided she wanted to go to the local high school for educational and social reasons (she wanted to join teams and was on the cross-country and track teams).
I think the bigger difference here in Georgia is that the Baptist churches, while huge, are focused on religion as opposed to education, and not focused on athletics. That gives the local high schools the upper hand. And remember that a lot of people here in Georgia are transplants (myself included), and thus don't think about a school for their kids based on "our family went there."
I suspect that there is a lot of "gamesmanship" in recruiting, and kids' families may not have to live in the school district they play for, here in Georgia - I don't know.