Discrimination is allowed as long as it's in a church. Actually, most churches base their entire philosophy around it, so it makes sense. Same way they get away with being tax exempt even though they make more profit than any other business in the world. You won't win a battle with a church, they got the Christmaster general on their side. Look for a different job and forget about the EEOC rules. They clearly don't apply to religious organizations, nor do any other rules that the rest of us inferior sinners are forced to abide by.
I would have to say that if they are soliciting for the job on Monster, then your religion can't be a stipulation for hiring. That is discrimination based on religion. If you apply and are refused a job, and they tell you that you can't work there because you aren't said religion, you have a case. If you apply and they say thank you for your time, just walk away. You will have a very difficult/expensive time trying to prove discrimination in court.