What a lot of people don't understand is that 'Roe v Wade' wasn't explicitly about abortion. Yes, the case that was being litigated involved whether a doctor could perform an abortion or not, but the ruling applied to the rights of women (actually this would apply to anyone) to confidentially consult with their doctor and that the state had no right to interfere with a medical procedure being done for a medically valid reason. And since medical abortions, which over the years were recorded using various other medical terminology, had been performed when there was a medical reason, it was therefore a legitimate procedure. The court simply said that the state had no right to dictate what is or is not a medically valid reason. That was between the patient and their doctor, and NO one else.
Now for years, the Republican party, while they may have never been a champion of abortion rights, chose to just take no real stance on 'Roe v Wade' one way or the other since it complied with many of the principles traditionally espoused by the GOP. That is, personal privacy, personal responsibility, keeping the government out of the personal affairs of citizens, small government, etc. It wasn't until the Reagan era when the Religious Right went to the Republican party and explained that there was untapped riches to be had if they would simply come out against abortion (along with contraception and sex education). So it was for manna, pure and simple, that the GOP decided that, despite it going against their long held principles, they were going to be champions of the unborn (of course, once that baby was delivered, they were back to their personal responsibility and keeping the government out of the personal affairs of citizens crap).
BTW, some people have noted that overturning 'Roe v Wade' could be akin to killing the Goose that's laying the Golden eggs. Will the pro-life Right continue to pour millions into the coffers of the GOP once they get what they wanted? Of course, they could turn their focus to other 'social issues', like birthright citizenship, integrated schools (hell, for that matter, public education itself), racially mixed marriages, gay rights, Social Security, the ACA, Medicare/Medicaid, the IRS, etc. And if you want to go all out paranoid on this, IF the Supreme Court eventually rules that the Texas approach, making something a civil issue that any citizen can take to court rather than having a state make it criminal, what's to stop hard Right-leaning states from going after a few of those other 'social issues' in a similar manner?
But getting back to the actual 'law' established by 'Roe v Wade', if it's overturned, what does that do for this idea that a person can confidentially consult with their doctor over the types and reasons why they're having a medical procedure? Will people have to sign a government disclosure form whenever they visit their doctor. Now before someone says that will never happen, remember in 'Roe v Wade' when the judges were talking about the 'state', they were being literal since there is nothing in the Constitution which even mentions privacy, let alone medical procedures, the Supreme's explicitly said this applied to the STATES and not the federal government (which again at one time complied with Republican support for state's rights). That's why there has never been any serious attempt to introduce any anti-abortion legislation at the federal level because the courts have always said that this was an issue for the states to manage, and as long as 'Roe v Wade' was the law-of-the-land, a citizen's right to confidentially, when it came to medical procedures, was protected, so there was no need for any sort of 'freedom of choice' legislation at the federal level either.
Anyway, this is a lot more complicated than most people realize.