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.