This is a gross oversimplification. The war 160 years ago was about whether a state had the power to unilaterally withdraw itself from the Union. Nobody then or now seriously questions the basic idea that the feds are still supposed to be of very limited and enumerated powers with the vast residue of powers resting with the states. Nothing about the Civil War or anything else changed that basic structure of our government.
First, despite this argument from the left, there is absolutely no way that any state comes close to banning contraception, even in the absence of a Griswold case. No state in the 1960s seriously enforced their ancient bans on contraception. Griswold was a manufactured case to get the ruling from the Supreme Court. Nobody even then was in danger of being prosecuted for contraception use. Nobody besides the tiniest minority of people today seriously wants to ban contraception. This whole line is an entire red herring.
But even if not, this was addressed at oral argument by the State. Even if Griswold, or Obergefell, or Lawrence are reexamined or many of the other parade of horribles would be looked upon and asked to be overruled, the stare decisis factors counsel keeping them. Even if Obergefell, for example, was wrong as an original matter (which I believe it was) it created a settled, easily administrable body of law that many people have structured their lives around and rely upon. If I was a judge, believing as I do that Obergefell was wrongly decided, I would not overrule it for these reasons. Society needs stability.
Roe and Casey are unique in that the “right” they found derives from, let’s face it, nowhere, and that the constitutional argument to privacy or autonomy which would allow for abortion would logically have to allow for a host of undesirable things. The cases decided without support what the status of a fetus/unborn child was by simple judicial fiat and no serious analysis. Those are the types of cases that in order to preserve the legitimacy of the Court need to be overruled because with the stroke of a pen they subverted a facet of democracy that rightfully belongs to the people themselves to decide at the ballot box.
She did not say that “forced pregnancy is like vaccines.” A good argument does not begin by misstating the argument. The basic ten second soundbite is that “a woman has a right to choose what to do with her own body.” A mandatory vaccine is but one example to say, “No she doesn’t.” Jury service, conscription, witness subpoenas, prohibitions on recreational drug use, incest laws, seat belt laws, and drinking age laws are but a few more examples that destroy such a bald declaration that our Constitution provides absolute bodily autonomy in law. You can argue differences between those things and pregnancy, just like you can argue differences between any two things, but the general principle of bodily autonomy has failed. One must then present a different argument that is more focused and also supported by text, history, and/or tradition. The right to elective abortion simply fails that test by any measure.