Are you willing to take the inversion of your position: that you should have no ability to control what information the state exposes your children to?

What about media with sexual content? Or content that promotes creationism or the idea that there are two biological sexes, which were created by God?

My position is balance between the family and the state for the maximal benefit of the child.

Also the balance should be towards access to information. There is no symmetry between exposure to harmful ideas and restricting good ones. With your example of two biological sexes created by God it is pretty easy to explain that the reality is more nuanced. If parents restrict access to information and the state doesn't intervene, the harm is bigger.