I think it's more accurate to say that some forms of classicism, and 19th century German Romanticism, were broadly part of an anti-modernist sentiment which was definitely part of a fertile ground in which fascism was able to take hold. That isn't to say that all 19th century and early 20th century romanticists or fellow travelers were authoritarian or fascist, but that material was often used by people who were.

And it doesn't help that at that time universities and the study of classics was basically the preserve of the upper classes, who naturally had elitist ideological biases.

There was definitely a sense among many that modernity, democracy, multiculturalism, liberalism were tied up with and responsible for the chaos in Europe at the time. And fingers were pointed at communists, socialists, Jews, liberals, secularists, etc, and in that period nationalists and ultimately fascists or other ultranationalist authoritarians were able to take root. And they often did so by appealing to their imagination of the past.