You could raise a stink but I suspect that, in the end, your better off just taking your lumps and moving on.

The motivation for treating you differently could be any number of reasons. They could have thought your smuggling in food or drinks. Most movie theaters make a good part of their money at the snack bar and, even though I have never run afoul of them, I suspect that theaters try to discourage the import of food and drink.

Large bags may also be discouraged for showings that are full to limit conflicts and to speed the movement into and out of the theater. There may even be applicable fire laws.

There may also be some discrimination based on the perception of a male carrying what might be considered a 'purse' as gay. I had a friend who was beat up because he carried a 'purse'. In reality the guy is a diabetic and his 'purse' contained his meter, insulin and syringes. Bigots tend to overlook alternative explanations. Then again what a person's orientation may be shouldn't be an issue and if a guy wants to carry a bag people shouldn't read anything into it.

An alternative explanation might be that the manager has been overzealous in applying the warnings of anti-terrorism alerts. People bringing bulky bags into paces of assembly might, in some settings and times, be looked upon with suspicion. Packs, bags and anything but the smallest hand bags are often excluded in government buildings.

There is also a issue with homeless people coming in to hang out and enjoy the AC. Once in they sneak from theater to theater to maximize their time while limiting the cost. Such patrons have a tendency to be disruptive and unpredictable.

Any, all, or none, of these explanations may apply. I think your within your rights to complain. A corporate run theater might best be addressed by way of their corporate office. The managers are largely figureheads. If the theater is locally owned You could speak to the owner. But I suspect that, at best, you get a polite brush-off and a movie pass. Hardly worth the time and effort in my book.