The age that a child has the right to privacy is 18 years of age and under age 18 the child has no constitutional right to privacy as long as they are living with their parents.
Parents can invade their children's privacy as long as they are under 18 years of age.
If the child is under 18 and their parents are responsible for them the parents have a legal right to invade their children's privacy and doing so can help to protect their children from any possible harm.
While children may not like their parents invading their privacy and going through their things there is nothing illegal about the parents going through their children's belongings and invading their privacy.
My parents would always rummage through my things until I was 18 and although I hated it I now understand why they were doing it and it was to protect me.
For example a parent may rummage through their child's things to ensure they are not hiding things such as drugs or other illegal things.
You only have a right to privacy 100 percent when you move out on your own.
Or when you turn 18 then you have a right to privacy although some parents will give their children more privacy once they reach 14 to 15 years of age.
Until you move out though there's not much you can do to prevent your parents from invading your privacy as long as you live under their roof you have to follow your parents rules.