It might be easier to try detection (and embarrassing alarms) instead of physical prevention. For example, floor sensors could detect when multiple sets of feet are enter on the same activation.
Granted, they might not know the difference between one person and a handcart versus two people where one is in a wheelchair, but I doubt many would-be infiltrators would draw attention to themselves that way.
I know for a fact that people will ignore it and set off the alarm anyway even with a large sign covering the entire top half of the door. Then the alarm goes off so often that all the bystanders ignore it too, so there really is no point.
Granted, they might not know the difference between one person and a handcart versus two people where one is in a wheelchair, but I doubt many would-be infiltrators would draw attention to themselves that way.