Libertarian socialism is leftist because its goal is to replace capitalism (that is, the ownership of the means of production by elite capitalists) by the collective democratic ownership and management of capital. It is basically an anti-authoritarian version of capitalism (as are many anarchist philosophies.)
OK, communists suppressed free unions, but if you look at the most leftist democratic countries today, like in Scandinavia, 80% of the working population is unionized. Free unions and economic equality are a major part of leftist economic ideology. So Nazism was leftist in one economic respect but not others, and was rightist in terms of nationalism (and for that matter, social conservatism — they were against toeiva and were anti-feminist and pronatalist.)
People who identify as mainstream conservatives should not feel hurt when people point out the threat from far-right extremism. They have almost nothing in common ideologically (perhaps aside from liking Trump). But for some reason they seem to want to minimize the threat (just as nonviolent leftists are reluctant to acknowledge the real threat from left-wing extremism). It’s a psychological thing, I guess.
We should focus on Torah and mitzvos and our avodas Hashem this world–timeless things of eternal value–and not focus on identifying with and debating all these transient political movements and ideologies.
We would all benefit from reading Koheles every day, not just once a year. Debating politics all day, as many people do nowadays, is truly havel havalim. It is like obsessing over palace intrigues. How much Torah could we have learned instead of squabbling about meaningless details? Rachmana litzlan.