Perhaps this is an American way of thinking, but I always thought that "throne" would be inextricable from "altar." When I think of famous 'atheists' from ye olden days I automatically think of Thomas Paine and Voltaire, who railed against the ancien regimes of their respective countries (of origin) and, at least in Paine's case, against the 'divine right of kings' in general.
My dim impression of the mid-late 19th century is that Darwin came along, along with various other thinkers, and there was a massive upsurge of atheism, agnosticism, skepticism, and general secularism, at least among the elites. And yet it took until the Great War for the "Crowned Heads" to either take a backseat or to be deposed altogether. Whereas in feudal times, and into the Renaissance/Reformation and Baroque eras, the kingpin (pun intended) to the whole thing, from the Holy Roman Emperor all the way down to the pettiest baronet, was "divine right."
How off are my assumptions? And how much of a threat was the rising tide of secularism to the institution of royalty/aristocracy prior to the Great War?
Not necessarily. The concept that you're interested in here is "Social Darwinism". From Encyclopedia Britannica:
Social Darwinism, the theory that persons, groups, and races are subject to the same laws of natural selection as Charles Darwin had perceived in plants and animals in nature. According to the theory, which was popular in the late 19th and early 20th centuries, the weak were diminished and their cultures delimited, while the strong grew in power and in cultural influence over the weak. Social Darwinists held that the life of humans in society was a struggle for existence ruled by “survival of the fittest,”
This is the ideology that elites used to justify their eliteness in the age of science and reason: "We're better than you because we're successful and you're not" instead of "We're better than you because God said so."
I should mention that this was most prominent in the capitalist United States as opposed to Europe (if this is false, please correct!).