Over time, I've tended to resist "slippery slope" arguments as applied to policy, and abortion was one of the obvious candidates for that rejection.
"If abortion is outlawed, or even regulated, women will have to report their menstrual cycles to the government and police will be rummaging through garbage to find the tampons to prove/disprove the reports" never struck me as obvious or inevitable, because we have historical examples of things running both ways.
In the US, prior to Roe v. Wade, I've never seen claims that there was any kind of universal "pre-crime" investigatory regime. The closest things I've seen are claims that Border Patrol would question young women crossing into Mexico on the possibility that they were going abroad to procure abortions. Other than that, it was more a matter of acting on reports ("I think my neighbor is running an abortion clinic out of his house").
On the other hand, the communist Ceausescu dictatorship in Romania does seem to have resembled that surveillance state prediction.
And I think there's good reason to believe that what's coming here and now in the US is closer to the Romanian experience than the pre-Roe US experience.
I have two reasons for thinking that.
One is that modern American "conservatism" has evolved over the last 30 years or so into something closely resembling East German communism, with Jesus rather than Honecker as General Secretary of the Party.
The median age in the US is about 38, which means most Americans weren't even born when Ronald Reagan and George HW Bush ran against each other in the 1980 Republican presidential primary in part on which was the more "open borders" (in those exact words) candidate.
That majority was also either not alive, or not of voting or typical "political awareness" age, during the period when "conservatives" were fairly united against the notion of a "national ID" to control internal travel and employment.
These days, "conservatives" largely support East-German-style border walls, Soviet-style internal passports ("REALID compliant" state-issued identification to travel by plane -- with bus and train in the works -- between states), universal "E-Verify" checks before you're allowed to work for a living, etc.
The intent to build a king-hell panopticon surveillance state is definitely there, where it doesn't seem to have been pre-Roe.
The other reason is that the means is increasingly there, as we've learned from e.g. Edward Snowden's disclosures of government eavesdropping, data mining, etc.
A few years ago there was quite a bit of talk about Google's advertising algorithm being able to figure out that women were pregnant before the women themselves knew -- the woman would start seeing advertisements for disposable diapers, car seats, etc. before she ever peed on a stick and saw a plus sign. If governments really want to enforce abortion bans, is there any real doubt that they'll seek access to such algorithms, or develop similar ones?
The slippery slope does seem to exist, and we seem to be more than halfway down it.
On the flip side, though, access to reasonably safe abortion, legal or not, is probably far closer to universal now than it was pre-Roe and will probably stay that way. In many cases, it's as simple as a pill, and government has proven itself incapable of suppressing traffic in pills for more than a century. Even "surgical" abortion is probably something that pretty much anyone can procure the basic equipment for (no more coathangers) and, I suspect, learn how to perform online. Maybe not as safe as with an MD at a clinic, but far safer than the kitchen table scene in If These Walls Could Talk. And there are ways to avoid all but the most specifically targeted government surveillance of one's browsing and purchasing and communications histories.
As Harry Browne pointed out a quarter of a century ago concerning government "wars" on domestic "problems," if government declares war on abortion it won't be long before men are having them. But, as with the war on drugs, the prisons will probably also be full of people accused of involvement in abortion, even as it remains available to anyone who wants it.
Which sounds like the worst of all possible worlds to me.
But to today's neo-Stalinist "conservatives," it probably sounds like utopia.