What about having IRL stores sell one-time use age verification tokens after showing ID? Just like tobacco or alcohol they can make it illegal to provide them to a minor. Whereas if you're worried about privacy you can still buy with cash.
Sure, it adds more steps than just "click this checkbox if you're an adult" but kids/teens are a crafty bunch and, unlike drugs and sex, a) the penalty for violation of the rules is not immediately obvious (to the youth, OR even to society) and b) the act of violating the rules is not obvious in itself to people who aren't on that person's phone: there's no physical items left behind for parents to notice.
Effectively what we're talking about here is trying to solve the Sybil Problem, which has no widely-accepted solution.
There's no database of alcohol or tobacco buyers. The sales clerk just checks your id and forgets about it. It's a code good for use on exactly one account on one service, and expires in maybe a year. If you have multiple accounts on multiple services, buy separate codes for each one. They should be reasonably priced - no more than $5 each.
You don't need a perfect solution. Despite laws against underage drinking, smoking, and drug use it still happens.
The store sells a scratch card containing a single-use code, after you show them ID. When you sign up with whatever social network, you enter the code and the social network validates it with the code provider service. That's it.
At best the code provider can tell the social network which store the code was purchased in. Drive over to the next state to purchase codes if you're paranoid. Mandate by law that no records of code purchases or copies of ID are kept. We don't require it for alcohol or tobacco purchases so there's no justification here.