A lot of the time, the measures the state needs to take to protect children includes protecting them from actions of parents that might very well be well-meaning, but just as clueless and easily manipulated by advertising as their children, but all to often even don't care.
While I'm for reducing the power of the state, protection of children is not something society can abdicate from without severe negative effects.
I will admit that this is a tricky area. Children are people and people certainly can choose to come to the aid of someone else who is being abused or harmed. But dealing with children is somewhat special, since it is generally considered the parent's responsibility and prerogative to decide how to raise their children.
Sadly I don't think there is any way to come to any real, objective answer on this issue. It is one, IMO, that will cause conflict as long as there are people.
While I'm for reducing the power of the state, protection of children is not something society can abdicate from without severe negative effects.