This argument is one that comes up a great deal by groups/organizations that don't support Open Adoption Records. The list is a long one. They use the same argument over and over. It has no legal standing. The right to privacy means protection from government intrusion. Yet adoptees are subject to government intrusion by having their adoption and birth records sealed.
Most of these groups feel that abortion will be affected by the changes in the law. In states and countries where there is open access to original birth certificates, there is no increase /decrease in abortion or adoption. They argue that women in adoption deserve the right to privacy just as those that have abortions.
Abortion is a medical and reproductive issue. It is a medical procedure. It is also a reproductive issue because the woman has sovereignty over her body. The woman has the right to decide at this point what she is going to do with the baby while it is in her body. It is her body after all.
Adoption is a legal issue. Labor and delivery is a medical procedure but it results in a living human being with the same rights as the mother. No one person has the right to reign over another person's life. They are both given equal representation under the law. Adoption is a legal procedure that occurs in a legal courtroom. Original birth certificates are not sealed at the relinquishment of the child but at the adoption proceeding itself. Original birth certificates belong to the person whose history it records. It doesn't belong to that person's parents, adoptive or natural. So its really the adoptee's right to privacy that are being violated, not a birthparent or adoptive parent.