In a legal sense, civil governance may intervene when a child faces aggression. This includes medical treatments not required to preserve health or normal development. Parents may authorize treatments such as removing a tumor or treating asthma---treatments that remove a threat to the child's health or restore normal bodily functions and development. By contrast, treatments that are purely cosmetic or that intentionally diverge from normal development fall outside parental authority and constitute aggression because children lack the capacity for informed consent to such treatments.
This does not mean granting the state sweeping authority to regulate health care through broad legislation. Protecting children requires restraint. The possibility of abuse should not be used as a pretext for expanding the role of civil governance from adjudicating aggression into usurping parental authority in all medical decisions for their children. That is a quick path to medical totalitarianism.
Recent controversies highlight both dangers. The "trans-kids" debate illustrates how life-altering procedures can be carried out without genuine informed consent or exaggerated threats to a child's health. Meanwhile, the COVID-19 pandemic showed how quickly the state's role in health can expand into coercive mandates over masks, closures, and vaccinations. Both demonstrate that centralized control erodes liberty without solving underlying problems.
Practically, given these dangers and the complexity of medical decisions, the better path is decentralization---limiting civil governance to its narrow role of addressing acts of aggression. By keeping its focus there, families and communities remain free to make their own health care choices.
This question is from Faith Seeking Freedom: Updated & Expanded, available in paperback, PDF, and Kindle.