On the basis of what single policy would you actually abandon your home, state or country?

Heh.  From The Liberals Threatening to Pick Up and Leave by Jerusalem Demsas.  The subheading is How abortion could scramble American geography.

It is a mainstay of American politics that when something goes against a certain class of interests, people threaten to leave America.  I suppose it is has some efficacy to the extent that it grants some gravitas to the the threat.  Who would wish to leave their natal country much less the most rewarding and free country in the world?

It is notable that the threat seems almost always to be from people on the Left.  I am sure that some people on the right must have made the claim at some point or another but I can think of neither individuals nor a time when it was a common threat.  I would guess that there might have been some such sentiments when Obama was elected in 2008 with his promises to fundamentally transform America, but I don't recall that being the case.

It is likely an asymmetric threat simply because of the category definitions.  People on the right are almost always and almost tautologically patriotic and with a great love of country.  Conceptually leaving their country would be almost impossible; certainly existential.  

While people on the left can also be patriotic and love their country, as a whole, I think those two attributes are both less salient and less strong at a population level.

Regardless of who thinks that it is worthwhile to make the threat, how many people follow through on it?  

In 2020, 6,705 Americans gave up their citizenship.  Meanwhile, 628,254 people became citizens in 2020.  Nearly 94 times as many people took citizenship as gave it up, offering a pretty resounding endorsement of American citizenship.

While firm numbers are lacking, it seems most people involved believe that a large, if not majority, of those giving up citizenship do so for tax reasons.  America, for a variety of reasons (primarily tax control and terrorism concerns), has in the past decade made it increasingly difficult to maintain personal financial relationships overseas.  

The Guardian pinpoints the inflection point where tax regulations began really driving the numbers.

Between 2000 and 2010 the total remained relatively steady at less than 1,000 people, but after FATCA came in, the numbers rose sharply to more than 5,000 in 2016.

A thinly sourced hypothesis, but not inconsistent with the known facts, would be that about 1,000 people a year renounce their citizenship for a variety of reasons including conscience or policy protest and that about 5,000 a year renounce it for financial considerations.

As Demsas notes, there have been earlier instances when people claimed that they would leave the country if X was elected or Y legislation passed.  

Certainly in 2016, there were scores of celebrities threatening (promising?) to leave the country were Trump elected.  As far as I am aware, none of them did.  I think there was an earlier wave of threats, perhaps with George W. Bush's election in 2000.  

Demsas is more focused on intra-US moves.  With the Dobbs decision, there are apparently many threats to leave red states to move to blue states.  How real are those promises?  Demsas addresses issues which he thinks would make it unlikely.

Without looking at any numbers, I would suspect that the threat could be real for a very small number of people but that it would not be visible in the large movements or people that occur anyway in any given year.  

13% of people (40 million) change address each year.  About 2% move between states in a year; about three quarters of a million people.  

Given that people move primarily for jobs, for family reasons, for education, etc. all powerful motives, what percentage of them would change those decisions based on Dobbs considerations.  Certainly conceivable but not likely to be many.  The graduating poli-sci major from Boston College might conceivably have been considering looking for a job in Texas and might change her mind.  But if the military is transferring you, if your employer is relocating you, if you are returning to your home state to care for an elderly relative, and given that universities are all in very blue cities or counties, I don't think that for those classes of people, Dobbs would make any difference.  

Demsas looks at the fundamentals though and the data and concludes.

I’m skeptical that abortion will similarly scramble the American urban landscape, however.

His argument:

The first reason to doubt that abortion restrictions will cause Americans to move in large numbers is that they haven’t done so already. Even before Dobbs, access to reproductive health care varied widely across states. Mississippi’s harsh legal landscape had permitted just one provider to continue operations. In Arizona, Texas, Arkansas, and Louisiana, state legislatures had enacted TRAP (targeted regulation of abortion providers) laws, which created onerous requirements for abortion providers. According to the Guttmacher Institute, “The number of Texas women whose closest abortion clinic was more than 100 miles away tripled” from 2013 to 2014 because of TRAP laws.

This divergence between red and blue states did not spur mass migration to the latter. In fact, the fastest-growing cities in 2020 were all in the Republican-dominated states of Texas, Arizona, Florida, Tennessee, and Idaho. According to Pew, from 2010 to 2020, the states that experienced above-average population growth were Utah, Idaho, Texas, North Dakota, Nevada, and Florida.

That's actually a pretty big reason.  He adds.

How heavily will American liberals weigh a possible future need against quality of life in the here and now? On the whole, left-leaning states have higher costs of living than right-leaning ones. Although wages may be higher in certain blue coastal cities, that premium is erased by the price of housing, transportation, child care, food, and other goods and services. One paper by the economists David Card, Jesse Rothstein, and Moises Yi found that larger and higher-earning areas (which tend to be Democratic) have much higher housing costs, “enough so to more than completely offset their larger effects on nominal earnings. Thus, movements to larger or to higher earnings locations mean reductions in real income.”

Although abortion is a common medical procedure, most women will never have one. But all women will need to keep up with the cost of living for wherever they choose to live. This is why declarations by Democratic governors that their states are “sanctuaries” or “safe havens” for women seeking abortion care ring hollow. They are havens in name only, if the fee for entry is a $700,000 home.

Demsas makes good points.  The central truth is that most people have very few or no "die on this hill" policy convictions.  Everything is a balance of trade-offs in which safer environments, lower cost of living, and better public services are the key flex points and which will almost always win out.  

I can think of no Blue States and certainly no Blue cities where the cost of living is lower than the US median, where crime is lower and where public services are recognizably better.  Until that changes, declarations that people will move based on the principle of abortion are, I think, misplaced.  

I wonder whether the threat/promise to leave one's state/country might not be just a variant of argument by emotional catastophizing that is so common.  Advocates who cannot make a moral or empirical case for their cause and therefore resort to emotionalism and extremism.