Arguments like this are very popular, but they rest on cherry-picking examples from fashion and on ignoring (or manipulating) the context behind their rise to prominence. I think the waistline is always used as an indicator because of the widespread belief that women's fashion historically was determined by male sexual desires, so therefore a period in which women's dress does not emphasize an hourglass figure with a small waist means that women are taking advantage of men's attention being diverted elsewhere to downplay their figures. But women's fashion was not solely about trying to appeal to men, and these periods do not show women's fashion being considered as hiding their sexuality. There are also a number of aspects of women's fashion that were seen as as disruptive as or more disruptive than altered waistlines - huge sleeves, hoop skirts, bustles, hobble skirts, etc.

I think we first have to ask: what makes a period "culturally stable" or "culturally unstable"? Even in times of peace, cultures have reformers agitating for change, members of society who are dissatisfied, people behaving in frowned-upon ways, other people complaining or mocking them, etc. The first stage of the Industrial Revolution (1760-1840) saw a tremendous amount of social upheaval, but the entire period didn't see fashion ignoring the (relatively) natural waistline, or the other things mentioned above as disruptive.

The High-Waisted Neoclassical and Regency Periods (1795-1825)

The high waistline of this era has its roots in the loose, sashed chemise gown of the 1780s. While some women did wear a more fitted version of the gown over ordinary low-waisted stays, the more daring wore it more loosely, and the waist crept upward under the sash in a strong rejection of the current fashionable silhouette. As knowledge of and interest in the chemise gown flooded out into wider society, we eventually see a slight rise in the fashionable waistline even in more ordinary dress by about 1790, culminating in the well-known high waistline around 1794-1795.

So on the one hand, yes, the most precipitous jump in the waistline does occur during the early years of the Revolution, but on the other, it comes about ultimately because of an interest in aristocratic dress, which was itself challenging the formality of Versailles. (We can page /u/kittydentures for a much better discussion of the origins and popularity of the chemise gown, though, because it's more complicated than this.)

And as you can see in the subject heading, the high waistline outlasted not only the Revolution itself, but the Napoleonic Wars as well. I don't think there's any good correlation between cultural stability/instability to be made here - France was arguably unstable from the Revolution to the reign of Napoleon III (1852-1870), or through his reign, yet from 1825/1830 through the end of the century the waistline was at the natural level or reasonably close to it. Meanwhile, through the high-waisted period, Britain and America were comparatively culturally stable, inasmuch as any culture is actually "stable".

The Low-Waisted/Waistless 1920s

The waistlessness of the 1920s really has its origin in the early 1910s, when the high waistlines and narrow skirts of the above period were imitated. High fashion embraced the look from 1909 (though it can be seen as early as 1907) without retaining the tremendous bust uplift of the 1800s-1820s, and over the next few years it became standard. When the waist came back down again in 1915-1916, it remained loose and sometimes even fairly low on the top of the hips, while the bust continued to be underplayed. This aesthetic continued into the early 1920s, and while many women in the decade wore completely tubular slip-on dresses, there was also a type of dress with a full, supported skirt and a more natural waist sometimes called a robe de style.

So, again, we have the problem of defining how this relates to cultural stability. If it's WWI that caused the instability leading to the loose, natural/low waistline of the late 1910s, why does the opposite occur during WWII? We also see the waistline returning to its place across the board and becoming more of a focus of the silhouette in 1930-1931, at the beginning of the Depression, which was hardly a stable time. I also don't know how much of the full decade 1920-1929 can be considered unstable, as the great shakeups were occurring at the very beginning of it.

It's really tempting to try to draw correlations between fashion and things like "stability" (there's another old chestnut that the fashionable skirt length reflects the economy, sometimes argued as short -> good times and sometimes short -> poor times), but they only work by painting with a broad brush, defining terms narrowly, cherry-picking, and ignoring other context that gets in the way.