The belief/disbelief in this binary plays little, if any, part in my sense of anarchy. The short of it is that I dislike the worldview it arises within and within which it finds its relevance. And I don't find the notion of 'free will' all that anarchic.
When people use this binary it may be helpful to question them:
Are you speaking of absolute Freedom? If yes, how is this possible as sensuous bodies always somewhere, conditioned, whereas 'absolute' has always tried to mean that which is unconditioned?
If no, are you speaking of a kinda/sorta freedom qualified as 'within reason,' that is, determined by some sorta fuzzy limitation? What are these determinations? How do you come to know them? How can they be non-arbitrary determinations?
And so on...
1. What I've usually experienced is a conviction based in absolutes or a confusion of that conviction mixed with a loose determinism; clinging emotionally to an absurd (anti-?)concept while rationally contradicting that concept; conditioning what's held to be unconditional ('absolute').
Additionally, the notion of 'free will' is based in 'the law of identity (A=A),' that 'A' (or 'I') is or may be a thing-which-acts, a thing-in-itself-which-causes-effects. This further presupposes yet another binarism between body and ____: soul, mind, spirit, genes, etc., since 'the body' changes without our will, consent, our 'causing' to happen, 'its' dependent upon food, water, sex, sensuousness, which these type of folks often try to distance themselves from with lingo like 'the senses'. 'The body' thus cannot be included...but one simply can't move where one 'wills' without one. I've yet to encounter a disembodied 'will.'
It's left to the interlocutor to fill us in on exactly 'what' this really real 'A' is and where it lives. I've found they usually decline, particularly if they're humanists. At least the more theistic of the lot will admit to a soul-concept.
2. I don't find the notion of 'free will' all that anarchic despite all the pretense to the contrary, primarily due to the competitive worldview within which arises. There seems to me a concomitant hierarchy between the 'A' which 'causes' and that which is 'effected.' Most often (in my experience) this is held as another 'A': 'nature,' 'animals,' 'plants' 'the poor,' 'citizens,' 'labor,' etc. Whichever 'A' is effected is never on the level of 'A' The Causal Agent. If the Agent 'effects' then they win; if they fail, they lose.
This is particularly the case when it comes to the concept 'Nature' which is most often held as the uniform, law-driven, backdrop for every 'agent,' the stuff every 'A' utilizes and witnesses the effects of our causing that shit to happen. Sure, we may recognize other 'free willing A's' but only finding our 'equal' after plowing through the dirt of the world, and/or transcending it, pulling ourselves up by our proverbial bootstraps out of its mud; or in a slightly more collectivist version we are each 'human' and our kind is top-dog here on Battlefield Earth. No matter. The stench of hierarchy is pervasive: man (as an agent or as collective) vs. nature - either superiority over 'nature' according to The Word (of God) or 'within' nature according to 'natural law.' It's all the same stinky pecking order in either case: the 'freedom' of the master over the slave.
Frankly, I loathe the notion of 'free will' and the binary it rides in on.