FWIW, I typically wear Tevas (sturdy rubber hiking sandals with quick-drying velcro straps - tendinitis prevents me from going barefoot) to the water parks. They do double duty as my frequent footwear to the theme parks, as well, saving some extra space in my suitcase.
So far I've been allowed to leave them on, or in a few cases instructed to slip them off and hold them to my chest, on all the water park attractions, although I can't say what the policy is on that highest slide at Blizzard Beach, as I didn't attempt it.
I just make sure to give them a good rinse in the shower before we go, so the chlorine doesn't damage them.