The fact that Rightwing political philosophy follows a top-down hierarchy can in no way include Socialism with is all about equality. Equality is horizontal.
Fascism, NAZIsm are both top-down hierarchies because the top people in these groups actually belive there are other people beneath them - literally.
The only people pushing the Athenian Straw Man Nonexistent Threat of Slippery Slope Windyfoggery (ASMNSSW) RE DEMOCRACY are people who have a misunderstanding/problem or hatred of democracy. (See AUTHORITARIANS)