While a school may be "public property" that does not mean it is open to the general public at all times. The library is "public property," yet it has hours of attendance and rules. Parks are also "public property," yet they, too, have rules governing use and access including times. Schools also have rules governing who can access and when - visitors are generally not permitted to wander onto school grounds willy-nilly, they must check in at the office or follow other guidelines. You get the idea ...
In my state schools can prohibit entry to most anyone when school is not in session. I strongly suspect that the law is similar in most - perhaps ALL - states, even if it is not a law that is universally enforced by the police. The school can control access if it so chooses. If the parents don't like that rule, they can address it with the school administration, the superintendent, or the school board.