My husband and I created a FB page for our son (he’s almost three months) simply because the opposite happened to us. The birth parents’ extended family members were finding us on FB and friend requesting us. It put US in an uncomfortable position because we didn’t want to be rude and deny the request, but we also don’t want them knowing all of our business.
As a happy medium, I created an email account and FB page for our son. The only people that we allow to be his friends are his relatives (our families and his birth family). That way they can see pictures and videos of him, and I can post cute status updates, but it keeps our personal pages our own. Our son’s page has no information on it (other than his birth day). It doesn’t even say where he lives.
It works for us and was a great way to meet everyone’s needs. When he gets older, he can email them through his address if he wants, and they know they can email him through that address as well. They’ve been using it and more and more of their extended family members have been requesting friendship with him.

Cathy