When you really think about what a classless society means, it's kind of frightening.
Tangentially, I really do wish we would stop trying to plot totally different paradigms on the same spectrum. The vast majority of everyone will share the common sense idea that the structures of society have been important in the advancement of the species, that advancements in culture and government and economics as well as technology have gotten people from nomadic tribes that slaughter one another to modern society.
The fringe groups that are typically seen as extremists aren't just really far right or really far left, their ideologies exist in a parallel universe where the foundations of our society are the root issue; where civilized society and governance aren't solutions to conflict or suffering, but instead the cause of those problems. That's where you get the anarchists who want governments to disappear and let human nature run free, the communists who seek to replace all aspects of human civilization with a single monolithic thing, and the fascists who see the conflict and instead of trying to fix it, they decide they're gonna win.
But normal people don't view the world that way. Normal people know that suffering is natural and society works to mitigate it. Normal people know that conflict is human nature and would exist with or without power hierarchies. Normal people believe that good is done through wealth, and government, and leadership, and that it's not all just some arbitrary system of oppression. If someone isn't on board with the idea that the state, the economy, and the structures of society in total are just systems of oppression, then it doesn't matter how far left they go, they still won't reach communism.
Edit to summarize: I think when discussing left to right politics, it would be better to limit it to the discussion on what form and scope of government is most beneficial, and ignore all the groups who think it just isn't.