"Couldn’t the state express an interest in regulating what health care providers do, apart from whether the patient requests the intervention? I am thinking of assisted suicide, where physician care is regulated by the state, but I guess the same could be said of abortion. A state could say abortion or assisted suicide is a procedure that we don’t want our physicians or nurses to provide, with no criminal conduct attached to the request, only to those who perform the procedure. I am no fan of abortion controls, but would imagine the argument could be made. Would be interested in your views."
The Rosetta Stone for such things, I think, is Griswold v. Connecticut. I like Justice Harlan's approach to that case best - I liked Justice Harlan's approach to MOST cases best - but Justice Douglas handled the issue at hand in the majority opinion:
"In a long series of cases, this Court has held that, where fundamental personal liberties are involved, they may not be abridged by the States simply on a showing that a regulatory statute has some rational relationship to the effectuation of a proper state purpose."
This issue is actually before the Court in Woman's Health v. Hellerstedt, which is sub judice right now. That's the Texas case testing whether the restrictions put on places where abortions are performed are constitutional. I think the state's arguments follow the line in my friend's comment. Those arguments can certainly be made. Whether they will stand up remains to be seen.
As regards the original post, however, I think the pro-life movement has a lot riding on the moral claim that abortion is murder, and while some may applaud anything that saves what they view as unborn lives, others will bridle righteously at the idea that the state has a rational interest in making the taking of such lives safe. In passing such a law, the state appears to legitimize abortion itself. Indeed, with the details unstated, the Texas legislature's position is indistinguishable from Bill Clinton's, viz., that abortion should be safe, legal, and rare. A candidate who advances that argument is not a "true" pro-lifer.
Assisted suicide is a good template, except that the victim is also a co-conspirator. No one is allowed to participate in an assisted suicide, and the state can argue, rationally (if not necessarily persuasively) that the opportunity to raise "assisted suicide" as a defense (think reasonable doubt) in a homicide case makes legalized assisted suicide unworkable. I don't see an analog to that argument in the abortion scenario: the mother is available to testify, and Roe v. Wade has already determined that the (timely) aborted fetus is not the object of criminal conduct. The state needs a rational reason not to allow a doctor to perform any particular procedure, and, under Griswold, where that procedure serves a fundamental right of the patient requesting it, which, under Roe v. Wade, an abortion in the first trimester does as a matter of law, the reason must be more than rational; it must be compelling.
My friend's comment may point to the Hippocratic Oath and who gets to enforce it. Do abortionists violate their pledge to "do no harm"? (Hippocrates thought so, but things change.) Can the state make adherence to the oath, as interpreted by the legislature, a condition of licensure? Can it make adherence to the oath as interpreted by anyone other than the doctor and his patient (the fetal carrier) a condition of licensure?
But once again, how can harm be done without the co-conspirators being liable for doing such harm? We cannot create a fiction that the abortion harms the mother in ways she does not understand, because that would require admitting that the abortion does not harm the life represented by the fetus, and once again, the pro-life linchpin is removed.