I believe this argument is not about a grandparent being proud and sharing a photo. I believe it is about the son being upset that his child was being exposed to someone who he didn't want his child exposed to. In this case, yes it is a baby. But the if he chooses to be estranged (him and his child) from his sibling and the baby, that is his choice and everyone must respect that.
I am a bit shocked by the boundaries talk on this thread. Adults have the right to set boundaries. Both for themselves and for their minor children. We do not have to like them, we do not have to agree with them, but we do have to respect them. Does not matter how ridiculous we think they are. If we don't there may be consequences.
If I were told "in my house, its my rules" with my child, then my child you not be at that house long. This is not giving ice cream and sweets for dinner. This is involving a 4 year old in family drama against the parents wishes.
I do believe that the son is being unreasonable by asking parents to take a side. Of course a parent would not choose one child over another. But I do not think he is being unreasonable to ask that the OP not share photos of his child with someone he wants to be no contact with.
As for the gift thing. Unless he has specifically asked you not to send them, then send them. If he has asked you to not send anything, then do not do it.