Except it doesn't fall into that category.
It's a parenting decision and falls squarely into the 'what kiddo is involved in/who kiddo hangs out with on one parent's time is between kiddo and that parent'.
I agree with you on this.
My grandson is posted all over FB pages of people associated with his dad. My daughter has no say over that, dad gives his permission for them to post and they can.
My daughter does not agree with what dad is allowing. She posts nothing on her FB concerning the child and she asks friends and family to not either.
Instead we have a family FB page, it's private, the child is almost 8 and he can access it himself from computers in her home, or grandparents home. He does not know the passwords.
It's none of dads business what is on that page, its about her time with the child. Eventually the child will be old enough to have his own page.
If she allows it, that is her business, her time with the child, her parenting decision. It's not a joint decision, it's up to her to parent the page on her time, just like it would be up to dad to do the same with anything set up in his home.
Why is this being looked at different. It should be considered one of those things, that you just have to trust the other parent to do their job on their time. Otherwise many of these parenting differences need to be looked at again and considered to be major decisions.