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"Contrary to a 'horseshoe' theory, the evidence reveals increasing antisemitism moving from left to right."
(64.media.tumblr.com)
Hersh, Eitan; Royden, Laura (25 June 2022). "Antisemitic Attitudes Across the Ideological Spectrum" Political Research Quarterly.
doi:10.1177/10659129221111081
Do you consider anarchists and anarchocommunists to be extremists? Or authoritarian?
Extremists? Sure - they are, by definition, as they are outside of normal, status quo political ideologies. Authoritarian? No of course not. Anarchists are anti-authoritarian. I'm only saying that past communist states (namely PRC and USSR) have been authoritarian and fascist states have also been authoritarian.
Obviously modern neoliberal states are also authoritarian, but the classic horseshoe is almost exclusively applied to fascism and communism. Since it is incoherent as a political theory, I'm sure you could apply it similarly to any polar opposite ideologies and come up with something they share in common.
You might want to consider that those who call themselves leftist may not actually be leftist.
For instance, "Nazi" is short for "national socialist". They are clearly right wing, however, if you pay attention to their actions.
So-called socialist states are generally deeply repressive and that is not left wing. They were better at branding than the Nazis, but for instance the USSR neutered the soviets - the workers' councils after which the state was named - very soon after taking power. The state owned rhe means of production, not the workers. It was state capitalist. After that workers had to strike just like under any other capitalist regime, and they were brutally repressed by the state.
Under no honest description of socialist does that qualify. So they failed on both the "Soviet" and "Socialist" parts of their name.
Horseshoe theory is just capitalists happily buying into the USSR and other state capitalists' self mythology about being socialist because it's good propaganda to scare the workers they rule over into believing that there is no alternative to neoliberalism's stochastic brutality.
If we understand "Leftism" to be about a relationship to the means of production - namely one in which the workers/plroletarian class owns the means of production - then the USSR certainly was socialist/leftist to a significant degree.
Since leftism is about that relationship to the means of production, that also means that a government can be both Leftist and Authoritarian. We can discuss to what degree an ideal leftist government should be "authoritarian", but that is less a conversation about the economic aspects of leftist political ideology and more about the political philosophy around personal freedoms, freedom of speech, etc. - none of which are completely cut & dry.
One could easily argue that some degree of "authoritarianism" is necessary to protect greater freedoms at the expense of lesser ones - that could be a coherent pro personal freedom and pro authoritarian argument. One could also argue that the anarchist conception of personal freedom is doomed to fail without an "authoritarian" power hierarchy to protect those freedoms. All I'm saying is the question of to what degree the power of the state should be limited is by no means answered.
Ownership means having power, having control, over the thing you own.
An authoritarian government that maintains control over the means of production, no matter how much they nominally "belong" to the workers, inherently alienates the workers from having power and therefore from ownership. In that sense it is state capitalist.
You cannot have it both ways unless you change the meaning of words like "own", or "authority". Your own description of leftism precludes authoritarian methods.