When airport security was making people drink from opened containers they were carrying, it was an effort to make sure that the containers really held beverages, and not flammable liquids that could be used to set a plane on fire. There was a huge outcry over an incident with a nursing mother carrying bottles of expressed breastmilk. She sued after she was forced to drink some of the milk, and that convinced security to drop the requirement.
Bag checks at Disney parks are only looking for weapons, alcohol, and/or glass containers. They will not stop you over food/soft drinks or make you discard them, unless your drink is in a glass bottle.