Maybe I can provide a different perspective here. We too recently moved from a major metropolitan northern city to a rural town smack in the bible belt. When I read the OP, it was uncanny how similar some of the OP's experiences have been to ours.
I can only describe the experience as INTENSE in regards to religion down here. There is great pressure to attend church, not only on Sundays, but also Wed evenings, Sunday school, Sunday regular service, and Sunday evening service. To just attend regular service isn't enough. You're viewed as different and not fitting in if you differ from what is done here. Yes, the OP wasn't joking, its true that everyone's first question is "what church do you attend".
I understand the OP's tone of frustration. I also am not used to the outright blending of religion and school functions. When we attended a baseball informative parents session, we all had to pray before the meeting. I've never encountered this before. Yes, emails from this particular coach had religious phrasings in it. Right or wrong, its not what we're used to and therefore seems strange. We've gotten used to it over time.
If you go out to lunch with someone, you pray before eating. Thats something we weren't used to also. I think overall its a major culture shock that the OP is experiencing. While it may feel strange to him/her or that this is all being forced upon him/her, I'm sure they still want to fit in and belong. When towns are small and you want you and your kids to adjust, fit in, and not be shunned, you don't take a stand...you try to blend in as best you can. Its very much a different culture down here. Its very, very different from the north. Its easy to say how you should speak up and say whats on your mind, but when you're not living in it, its easier said than done.