I don't have a problem with this, as long as they pay the same as every other group.
Firstly, I don't have a problem with them renting the pool for this as a private function if, just as you say, they pay what every other group does. But I disagree that one religious observance should be disallowed over another. If the Church group that wanted to use the pool for a private function wanted to use it for a baptism what does that matter? It's not being done privately, and it's not being endorsed by the city. So why would you allow one religious observance over another? Seems inconsistent to me.
Well, ok, I see your point