Your son is visiting the problems of adults on the child. He needs to ask himself what makes a child “his”? From my point of view, biology doesn’t make a family. Love does. All of you have loved and nurtured this baby for this important first year. I see no reason for your son — or you — to abandon him because of his gene pool.
The child probably will need you all more than ever once he understands the complicated nature of his birth. Once your son gets over his very understandable hurt and anger over the betrayal by his girlfriend, I hope he can “adopt” the boy as his own. I also hold out the hope that he and his girlfriend will get some counseling to see if they can repair their relationship — or at least to agree on how they are going to co-parent the baby.
It’s interesting to me that your son continues to ask you not to abandon him (an adult), but he is willing to abandon a baby and asking you to do the same. I think he has some growing up to do.
I wish you well.