I know there's a rule against editing a page's alignment but I think Khomeinism should be considered authleft (not all authleft is communism, as distributism, longism, and paternalistic conservatism prove), the economic system of Iran is very socialist in nature despite the anticommunist views. In fact "privatization" doesn't actually exist, it usually means selling it to another portion of government. Also, there's a lot of social welfare as well as an economic system built around smaller merchants and vendors rather than corporations.
I would recommend any republican or conservative who wants religious influence in government to take a nice long visit to a place like Iran or Saudi Arabia and see how good life is there (knowing them they would probably unironically agree)