https://www.washingtonpost.com/outlook/2020/02/05/right-needs-stop-falsely-claiming-that-nazis-were-socialists/
Right-wing is as right-wing does. The National Socialists of Germany (Nazis) were about as “socialist” as the Democratic People’s Republic of North Korea (DPRK) is “democratic.” Their names are simply regime propaganda meant to obscure what they’re doing and make themselves seem more likeable.
The Nazis created an industrial-scale system for imprisoning (and ultimately, exterminating) Jews, gypsies, socialists, communists, homosexuals, “asocials” (prostitutes, sexual deviants, etc.), “race-mixers,” “lifelong criminals,” non-German ethnicities, etc. etc. The separation and stigmatization of groups of people on the basis of culture/identity is a right-wing thing. Marx didn’t care about any of that.
Same analysis applies to the Communist Party of China (CCP). Is China actually trying to increase worker ownership of the means of production and make citizens financially equal? No.
China is enriching a tiny handful of politically-connected capitalists, while jailing and persecuting religious and economic minorities, rewriting history from a “national pride” angle, creating a cult of personality around Xi Jinping, and militarily threatening neighbors. Those are all far-right things. Despite its namesake, “Communist” China is actually a far-right nationalist Han-ethnocentric political system.