American conservatism is conserving a different political history than you find in Europe. "Way back when", America was a constitutional republic with a distinct federal government with distinct separation of powers. That's the "good old days" that are conserved in America.
So it's not "silly" except that the same word "conservative" means different things in different contexts. Though that's true of the words "liberal", "democratic", "federal", and "republican" for that matter.
But it is a little silly to have a "republican" party in countries (USA, France) where the monarchy is long gone.