The answer to the first statement is: NO NO WRONG WRONG WRONG. You're completely wrong. Of course the state has an obligation to intervene to prevent grievous harm--otherwise murder of children by their parents would be legal! Saying otherwise promotes a gross dereliction of the responsibility of society to its members.
The answer to the second statement, however, is: YES YES ABSOLUTELY OF COURSE. The proper role of the state in safeguarding its members requires it to actually pay attention to people of the appropriate professions who know how to safeguard people in the appropriate ways. In the case of gender identity issues, those people are medical and mental health professionals.
The issue isn't that the state doesn't have a say. The issue is that it's outrageous when the state abuses its powers, granted so that it can play a protective role, to cause harm instead, and in contradiction to the best standards of care.