This is simply false. There is ZERO right to privacy about regulating doctors doing other medical procedures and this would be no different. There is no right to privacy implied anywhere in the constitution for such a thing. It is totally manufactured. This has ZERO to do with whether or not abortion is murder and what good, moral, and wise policy should be.
From Wikipedia:
January 1973, the Supreme Court issued a 7–2 decision ruling that the Due Process Clause of the Fourteenth Amendment to the U.S. Constitution provides a "right to privacy" that protects a pregnant woman's right to choose whether or not to have an abortion. But it also ruled that this right is not absolute, and must be balanced against the government's interests in protecting women's health and protecting prenatal life.
My point is that there are 2 options to strike down Roe:
1. Abortion = murder, therfore, the interest in protecting prenatel life is higher than was originally ruled (a court may be tempted to say this as they can likely point to medical advances since 1973 as basis for the change).
2. The entire premise of the right to privacy is manufactured.
You could imagine there are a few nafka Minas to that.