If you are asked to leave and do not leave I can see you possibly being arrested for trespassing, but I fail to see what you would be arrested for by bringing in food from outside the theatre. Sure, they could ban you from coming back to property (and this could lead to trespassing arrests, if you did return) but thats about it.
Much like cinemas. If I try to bring in food I didn't bought at the cinema store, I will be stopped at ticket check and refused entry. Also, the cinema doesn't require me to buy food as a condition for watching the movie. If they did, I'd consider it the price of entry.
What current ad-loaded websites are doing is the equivalent of letting you in to watch a movie, and then having someone come to you as you're watching, and poke you and yell at you because you didn't buy anything at the store.
> They can call the cops and have you arrested for accessing the theatre in contravention of the rule.
I've never heard of a cinema calling cops on people who snuck in food into the theatre. Is that US-specific?