Just curious. What are you worried about? I understand where children are adopted/ in care or where it would cause them embarrassment but if it isn't these what do you feel uncomfortable about?
When you put them on social media, you're allowing companies to deduce data about them. 'My gorgeous Sarah's birthday, 4 today!' - you've just told them that the girl in the photo is called Sarah, most likely your daughter, and they now know her date of birth. That's just from one image. Obviously, over time, they can start to deduce countless links about her lover of ballet, which girl guides group she's in, which school etc etc.
After a decade of that info, by the time they leave school, you've already sold their data down the river, albeit inadvertently.
I had this argument with my neice (I had industry knowledge of what was happening) and she couldn't fathom how Facebook and Google etc could really know this information, or how it could be a bad thing anyway. 10 years later, we now have Facebook grovelling on national TV adverts about how they've changed.
If you value your children's privacy, keep them off social media as much as you can. Sadly, it's a bit of a losing battle with almost every device wanting an 'account' these days. But don't give them any more than you have to.