Outside food and drink is not permitted at the Swan. The theatre states the reason without dressing it up: diner sales are what keep the business in operation.
That is the economics of every surviving drive-in. Ticket revenue is shared with distributors; the concession stand is the margin. A field full of families eating supermarket sandwiches is a drive-in that closes within a few seasons, which is broadly what happened to the several hundred Georgia drive-ins that no longer exist.
So the expectation is that you eat there. It is diner food at a drive-in: burgers, hot dogs, popcorn, fries, ice cream, fountain drinks. Nobody is pretending it is dinner at a restaurant on Main Street, and that is not what it is for.
Practical version: eat lightly beforehand if you want, but buy your food here. If somebody in the party has a genuine dietary requirement that the diner cannot meet, ask at the gate rather than smuggling.
It is a small thing to observe and it is the difference between this page still being accurate in ten years and not.