So you want to enable Family Sharing's "Ask to Buy" to buy feature but your child is on an old Apple ID and you can't find a way to go back and change their birthday to make it work? You're not alone. And while there's no easy fix, there is a way to work around it. As long as you've got an open on your Family Sharing account, you can swap your child's old Apple ID to a new child ID, and get Ask to Buy working the way you want it to.
It's important to note that this process can't convert your child's existing Apple ID into a child ID. It creates a new Apple ID and transfers all their data across. That means they won't lose any backups or purchases, but there are still some downsides. For one, they'll have a new email address, which means a new ID for mail, iMessage, and FaceTime. (You can forward email and enable multiple addresses for iMessage and FaceTime.)