LowePro sells an entire line of AW bags, which are normal camera bags with a pull-out raincoat, at prices ranging from $50 up through a few hundred, which work very well, and work as normal camera bags when you're not getting wet. Also, depending on your body and lens and their level of weather sealing, the only ride that may be an issue is Kali.
Splash Mountain you may get splashed but it's momentary, nothing a 70D or D7000 or better can't handle so long as you have a decent first party lens with some weather sealing (my D7200 and 16-85 handle it no problem), and Fantasmic doesn't get you wet at all. Kali you may come out dry, or completely soaked and drenched. LowePro's AW bags will keep your stuff dry during this, I've used them in pouring rain for hours and although I was soaked through my rain gear, my camera stayed dry.