I think your premise may be a bit off -- while it might be a bit tedious to play Revolution Olympics, there was certainly political instability among Protestant-majority countries in Europe during this time period, as well as before it. I think that you're comparing a country (France) that sowed a great deal of instability in the Napoleonic period when it conquered chunks of Europe (the revolution against French rule in Spain was directly related to its conquests there, for example) to a country (Britain) that had internal struggles that didn't boil over into rebellion in the home islands.

Whew, that was a lot of clauses. Anyhow.

The very obvious counter-example that comes to mind post-1750 is the rebellion in the Americas that resulted in the loss to Britain of what became the United States. In that conflict, of course, a majority Protestant group of colonies rebelled against its established Protestant government, but the British managed to hold on to not only Upper Canada and Lower Canada (that is, what's now Quebec -- originally a Catholic French colony), the Maritime Provinces, and their holdings in the Caribbean. This has traditionally been seen by historians as the breaking point between the First and Second British Empires, when the British refocused their expansion into India, Africa and the Pacific.

Keep in mind too that the American colonies had to an extent worked as a sort of "relief valve" where the losers of the various wars of the 17th century could go -- not only the ECW but the disagreements that preceded it, and the fallout from the Restoration and the Glorious Revolution.

It also seems like a bit of circular reasoning to say that the ECW doesn't count because it's the only event of its kind (cf. what i had to say above as the obvious "other" ECW, the American Revolution). The Restoration returned England to a monarchy, but a constitutional monarchy that was clearly subservient to Parliament and bound with strict constraints as to who would be able to serve as the monarch, up to the point where the royal family was imported from the Continent.

On top of that, during the Napoleonic period the internal politics of Britain were rocked by serious unrest and upheavals -- the entire Channel fleet, Britain's main defense against invasion, mutinied in 1797 and the mutiny was only put down by severe violence. The condition of the working classes in England during the Industrial Revolution was tenuous enough that the government feared for its safety on multiple occasions (keep in mind that Marx and Engels were radicalized in England); the series of Corn Laws can be seen as an attempt to offer relief short of revolution -- EP Thompson would certainly agree that the working class was made by its circumstances, but also made itself, in the struggles from 1780 onwards falling just short of revolution.

I believe the premise is slightly false.

Denmark had major power shifts in: 1770, 1784, and 1849.

Sweden had major power shifts in: 1719, 1772, and 1809.

The Netherlands had major power shifts in: 1747, 1795, 1806, 1815, 1830, 1848.

None of these events can compare with the French revolution, but nothing can, so the point is moot. I have been a bit liberal in my interpretation of a "major power shift", but I'm sure it's clear why each year was chosen if you google it.

This contrasts with France (French revolutions, restoration, Napoleons, five republics)

This really has more to do with the French Revolution and it's causes as opposed to Catholicism.

Italy (19th century turmoil, Mussolini).

Bear in mind that Italy, like Germany, only became a single, unified state in the 19th century.