It's legal for a Christian organization to require that. They can't make exceptions or pick and choose, but they can make it a bonafide requirement of working there. Like making all your staff be over 21 in a bar isn't age discrimination, or making all your locker room attendants be of the same gender as the locker they're working in isn't gender discrimination.

Does suck, though. I'd get the oogin's working in a place like that, frankly.