I wonder how this could possibly be enforced, considering that stage doors open directly to the public street and actors don't have many options for leaving the building. They could certainly post security at the doors to keep crowds moving, and I'm sure the stars will be hustled out right into their waiting cars, but what's to stop a fan from continuously milling about and stopping an actor on the sidewalk as they exit the building? Or following them down the street into the subway?
I guess, if the concern is strictly crowds, security could do that, but I'm thinking more of the general safety of the actors. A fan that knows that they can get a few moments with an actor at the stage door is less likely to then follow someone as they finish with the crowd and walk away from the building.
Maybe if actors exit masked, the more ardent fans won't recognize them.