No, Sauron is the same character I meant to talk about. The master of Saruman. Sauron is a theocratic dictator, and Saruman is, politically speaking, a Bishop-Duke. His ideology must be the same as Sauron's because he serves Sauron. And Sauron implements theocratic dictatorship in Isengard and Mordor. Theocratic dictatorship, as you must be aware, is a far right ideology. And nazis are also far right, but I'm not sure why they're the topic of discussion.

Nazism (/ˈnɑːtsɪzəm, ˈnæt-/ NA(H)T-siz-əm; also Naziism /-si.ɪzəm/),[1] the common name in English for National Socialism (German: Nationalsozialismus, German: [natsi̯oˈnaːlzotsi̯aˌlɪsmʊs] ⓘ), is the far-right totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany.

But really...

Never believe that anti-Semites are completely unaware of the absurdity of their replies. They know that their remarks are frivolous, open to challenge. But they are amusing themselves, for it is their adversary who is obliged to use words responsibly, since he believes in words. The anti-Semites have the right to play. They even like to play with discourse for, by giving ridiculous reasons, they discredit the seriousness of their interlocutors. They delight in acting in bad faith, since they seek not to persuade by sound argument but to intimidate and disconcert. If you press them too closely, they will abruptly fall silent, loftily indicating by some phrase that the time for argument is past.

— Jean-Paul Sartre