Conservatism has been those things many times and in many places. It's traditionally moderate liberalism. Conservatism in the US today is regressivism wearing a conservative hat for branding. Were the Nazis socialists? No, but it was in their name. Are conservatives conservative? No, they're authoritarian regressivists, because the goal isn't to be conservative. It's to be anti-progressive. But the conservative hat gives it recognizability and credibility.