The thing with anarchism (or communism, or many similar movements) is that it involves two stages. In the first stage, the existing system is torn down or removed, which is clearly a chaotic act. In the second stage, a new order arises; this new order is often lawful and almost never chaotic.
Except neither of those things are clearly chaotic or lawful.
Before you can have a real discussion of what alignment something is, you have to define terms. As is, Chaotic and Lawful have useless definitions in the PHB, and therefore mean absolutely nothing. You could describe essentially any action as Chaotic or Lawful... or even as both a paragon of law and a paragon of chaos
at the same time.
I would not be surprised if you could post your societies on various internet forum communities and get answers for every alignment for both of them, Libertad. And that, right there, should illustrate the problem with the PHB alignment definitions.
Actually, in this thread alone, with only
7 answering replies from a relatively close-knit community, I see
5 different alignments listed for society A. Society B
also included CE, CG, LE, LN, and LG (5 alignments from 7 respondents, covering all 4 extreme alignments!). That's a plainly horrific batting average, and clearly illustrates the point that with the alignment rules as written in the PHB, people are doing little more than playing a vague word association game where they just throw on a label however they feel like it, and players in game will have no idea what they can cast Dictum on without actually throwing down a detect spell even if they have intimate knowledge of the intended target's personality.
It's not even that the idea of alignment is that bad. It wouldn't actually be that hard to write more consistent and useful definitions. It's just that in the PHB it's written really, really badly... to the point of being utterly meaningless and arbitrary.