Actual post office or contract location? If contract location, I’d think not. If actual post office, it still seems shaky that they’d be able to tell Walgreen’s customers who have no business with the post office what they’re allowed to have in their car when they go to the drugstore.
It is actually a dedicated post office facility, it has its own entrance from the sidewalk and the normal signage on the doors and windows. I wouldn't think they would be able to enforce it there, but you never can tell, the law seems too vague in this case.