They probably don't allow then for safety and security reasons. Safety for you, other patrons and their equipment (slides, filters). Security for other patrons who don't want or don't know that their photo/video might be taken off them.
I've been there a few times. There are a lot of things they don't allow on the slides. Jewelry, phones. Most of this is for safety and I'm sure some for liability. If your phone or jewelry ended up getting into a filter there would be serious problems. There are places to take photos from outside and the end of the run.
I'm assuming a mix of people coming after them for damaged property and for safety reasons with necklaces/strings etc. The filter wouldn't be damaged from your stuff per say but the water slides do throw you into the water pretty forcefully at the very bottom. I would just assume its so people don't strangle themselves or step on earrings etc, or people in a frenzy over their phones/wedding rings being lost etc....
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