I don't find it much more surprising than, say, a 97% correlation between being male in one survey and male in another, or 'American' in one survey and 'American' in another, or 'Catholic' in one survey and the next. Political identity is deeply fundamental to people - 'politics is the mind-killer', remember?

A real-life example: the switch of the (white) US South from voting Democrat to voting Republican in early 1970s and forwards.

At least in the case of Goren's linked paper, an extremely high stability would be unsurprising since the data period is a fairly normal period: "data from the 1992–94–96 National Election Study panel survey" (although only fairly since this was, after all, during the Gingrich period).

Using the Libgen link above for Green et al 2002, you can verify that the 0.97 estimate is not a misquote, and by browsing the various tables, you can see that in all listed surveys the persistence of partisanship is extremely high. In fact, they also discuss your example, starting on pg85:

Because partisan attachments predict how individuals vote, the distribution of these attachments in the electorate has important consequences for election outcomes. Although the outcome of each election reflects the idiosyncrasies of personality, campaign events, and policy stances, it remains the case that candidates tend to fare better at the polls when their fellow partisans constitute a larger share of the electorate.

...This point is illustrated vividly by the partisan politics of the South. In the s, the overwhelming majority of Southern voters called themselves Democrats, and Republican candidates seldom won seats in the U.S. House. Indeed, recognizing their slim chances of victory in these Democratic strongholds, few Republicans bothered to run at all. A half century later, the situation is reversed, and Democrats struggle to field viable candidates in Republican enclaves from South Carolina to Texas.

[Table 4.1. How the Distribution of Party Identification Affected Presidential Voting, 1960 and 2000]

The influence of partisanship on presidential election outcomes can be illustrated by a counterfactual exercise. The election of  produced a dead heat between George W. Bush and Al Gore. Gore received .% of the vote, to Bush’s .%, only to lose narrowly in the Electoral College. In this election, according to the NES survey, Gore received % of the vote from Democrats, % from Independents, and % from Republicans.1 As shown in Table ., these numbers resemble voting patterns in , another close presidential contest between a sitting vice president, Richard Nixon, and a challenger, John F. Kennedy. Gore, although more successful in garnering votes from Democrats than Kennedy, labored under a disadvantage. Democrats comprised % of the voting electorate in  compared with % in . If the electorate of  had the same balance of Democrats, Republicans, and Independents as the electorate of , Gore would have won an additional % of the vote. Although the forgoing example artificially assumes that nothing about the contestants would have changed in a different partisan environment, the basic point remains: The relative proportions of Democrats and Republicans can be quite important politically. The significance of the partisan balance, which MacKuen, Erikson, and Stimson () have termed macropartisanship, is reflected in the intense scholarly interest in an array of interrelated research questions. How stable is the partisan balance, and to what extent does it change in the wake of economic downturns or political scandal? Are the misfortunes of the political parties inscribed in the allegiances of voters, and if so, for how long? If the aggregate distribution of partisanship varies over time, what does that suggest about the nature of individuals’ party attachments?

In this chapter, we take a closer look at the behavior of partisanship in the aggregate. Using summary statistics on the ratio of Democrats to Republicans, we show that the distribution of partisanship evolves slowly over time, both during and between election campaigns. When times are good, the partisan balance tips gradually in favor of the party that controls the White House; when scandal or economic downturn erodes presidential popularity, the outparty draws more adherents. Aggregate time-series analysis, in other words, allows us to better understand the “time shocks” that we posited in our investigation of individual-level panel data. The microlevel and macrolevel processes fit together in a coherent fashion.

Described in this way, macropartisan movement conjures images of a public rationally choosing its partisan allegiances on the basis of expectations about party competence, but one must bear in mind the sluggish pace with which this process unfolds over time. In the last chapter, we saw that time shocks of appreciable size rarely turn up in panel data. The present chapter underscores this point, showing that the aggregate distribution of partisanship seldom shifts abruptly. Instead, change tends to occur gradually, so that only dramatic changes in party fortunes sustained over long stretches of time are sufficient to produce politically significant swings in the balance of Democrats and Republicans. Even so, we find changes in economic performance and presidential popularity alone to be insufficient explanations for what are generally termed realignments. Although both factors played an important role in the transformation of Northern party loyalties during the New Deal and Southern party loyalties during the s, the partisan movement that occurred went beyond what can be explained by reference to short-term political conditions. To explain the magnitude of these changes, one must take into account the transformation of the social stereotypes of the parties, a theme to which we will return in Chapter .

That is, huge political re-alignments can be caused by subtle population shifts (because political races are typically decided by very tiny margins compared to the overall population; remember how few people even vote) over long time periods (because we telescope the time periods in retrospect), and so this is perfectly consistent with the extreme durability of partisan identity.

Can't say for sure without reading Green et al (edit: which I'll now do; thanks, Gwern!), but they're probably being run yearly. Assuming independence, a 3% year-on-year chance of changing parties gives roughly 20 years of stable party identification on average and 20% of all people sticking with the same party lifelong, which seems reasonable (though it's less than I was expecting).

In actuality, of course, these numbers aren't independent and a substantial portion of that variance is going to come from large-scale political events like the Southern shift you mentioned. That implies more stability in the absence of those shifts, though I don't think we have enough information to say how common lifelong party identification is. Intuitively I'd expect a lot more than 20%.