In fact, that would make any democrat (as in believer in democracy, not Democrat™) or republican (as in believer in a republic, not Republican™) leftists as well, since they believe in democracies or republics instead of a monarchy.

Or that’s what you’d think, but the guy who created conservatism was a monarchist trying to figure out a way for the aristocracy to exist within democracy. The right is stanning for monarchy under a different name, as proudly admitted by their ideological leader. For details look up Edmund Burke.