The food policy is there to stop people bringing in alcohol, glass, or anything else that cast members can see may be problematic. They never stopped us bringing food in, not even styrofoam containers of Chinese or Subway. The policy is simply there so if there IS something they want to say no to, they CAN. The policy is generally extremely lax in execution.
You can always bring in water bottles, and you definitely should! Freeze them the night before to keep them cool all day. Aside from that, my preferred beverage consumption method within the parks is to bring in a wide-mouthed reusable water bottle and ask for cups of ice water at counter service, and then if I want to go on a ride I'll just dump the beverage into the bottle.
Anaheim water is DISGUSTING unless it's ice cold. If you find the taste of the water gross but find carrying around bottled water is too heavy all day, bring Crystal Light or other water enhancers (next time we go we'll be making very concentrated iced tea and bringing it in a small bottle).
There are drinking fountains all over the parks, you're likely to find them near washrooms. Cast members can always point you in the direction of one.