Well. No. The sign doesn’t say you can not take photos of the church per se, what it says is that you can not take photos of the rituals that occur in the church or anywhere else in the grounds.
The statement in bold is probably the reason for the prohibition. One, the act of taking a photograph makes the religious act seem like a folk dance for the tourists. Two, since many of the followers are native Mayans, they do not want to feel like they are part of “Hey-Look-At-The-Natives!” photoshoot. Afterall, would you want someone to take a photo of you when you are in middle of church services. You know. Just as you are about to drink the wine in Mass, some person blinds you with flash and shouts, “Hold it! Don’t move! Awesome! He is doing something magical! Wow!”.
My Gramma never consented to her photo being taken. She was Cherokee. But one time my father was taking pictures of me in front of her bedroom window, and she was looking out at us. He got her in the frame, and took it. Nobody told her, or let her see it, and I think it was that fall she died.
I encountered this superstition Liberia. When we first got there we were warned not to take photographs of Liberians without their permission because there were still some tribal beliefs that taking a picture would steal their soul. The really interesting thing about this is that many of those people were willing to SELL you their “souls” for a couple of bucks.