Monarchy and fascism share some characteristics but the things that make fascism what it is don’t originate from Monarchism or a revanchism for monarchy in any sense. When fascism qua fascism arose in Europe it was a separate formation from monarchists, for example, who still existed in substantial numbers in those countries back then. Instead, fascism arose from declining material conditions in countries that were losing imperialist status, such as losing colonies or having large foreign debts after World War I, and this situation - and “solution” - were both highly capitalistic. Fascism recruits from the petty bourgeoisie for its foot soldiers at the behest of factions of the haute bourgeoisie.
Capitalism is proto-fascism. Fascism, to the extent that it exists beyond World War II, has often been reinvented for crises of capitalism, whether domestic or imposed through imperialism. And who did the fascists take so much inspuration? For the Nazis, it was the United States, a bourgeoisie democracy (capitalist) premised on genocide and slavery.
US whiteness is a social construct that serves to justify and reproduce marginalization: white supremacy. It started out excluding the Irish, Italians, the Spanish, Slavs, etc and shifted over time in order to maintain anti-blackness and anti-indigeneity. So it is far from just one thing and is simultaneously very recent. It would be best described as a culture of domination and capitalism, being a product of the US’ industrialization and then economic subjugation of the planet. Whiteness is about who you are better than and how entitled you are to a good life, or at least one better than non-whites. White culture is tolerating and even engaging in genocide so long as it is against non-whites. White culture is trying to pretend oppressions don’t need justice on any timeline that might inconvenience a white person. White culture is jingoist. The image of a warlike America has a white face.
As white people were largely drawn from European immigrants, they sometimes have watered-down elements of culture from “the old country”, Americanized to the point of being unrecognizable. Those elements were usually watered down because their immigrant ancestors were not considered white at the time so they tried to hide or erase identifiable cultural elements. Name changes. Modifications to food. Going to the whiter church. Skipping traditional holidays.
And of course, much is just white supremacy under capitalism. Processed industrialized foods. Commercialized holidays and events. Workaholic myths of paths to success. Everything cheaper or subsidized to their benefit and treated as an entitlement. National chauvinism and racist warmongering. Colonizer mindsets.