Actually it is their right to attempt to control what their own children have access to. I said check out but if the child wants to sit in a library - oh well. The only discretion the school has is availability not force other than actual text books.
The school unquestionably has the authority and discretion to ignore whatever nonsense a parent says and check a book out to a child. A parent has no power or authority over a school library or school librarian. Why would being a parent mean you got to be the librarian's boss? That's moronic
Again there is no point in this discussion we agree to disagree and you need to understand that most things in life are black and white and there are many variables and nuances.
But the question of whether or not a parent gets to decide which books a librarian checks out to a child does indeed have an answer. That answer is no, which is how it should be
No they do not. Only when it comes to curriculum and then parents can opt their child out. Protecting ones own rights does not mean you are now the boss or control of anyone else. We are talking control of the child not the school.
The school librarian is under zero occupational, moral, or ethical obligation to deny access to reading material to a child just because some guy says so.