Here are some elements of my attempt to put acceptability/unacceptability conditions in a broader context.
(1) The broad relevant “circumstance” of acceptability/unacceptability conditions is that of collective decision-making.
(2) In this context, there are always broadly personal-respect-based considerations that weigh against pressing good reasons in pursuit of truth (or having the substantively best decision be made). There is the possibility of it being best to, say, press a good reason less hard than one might out of politeness, at some small expense to the likelihood of the process yielding a substantively good decision. And we might build such respectful restraint in the presentation of reasons (at some small cost to relevant good decision-making) into a model of overall good collective decision-making.
(3) Sometimes these considerations of personal respect rise to the level of moral obligations not to present or press certain reasons. When this is the case, we have personal-respect-based unacceptability conditions on what reasons one is permitted to present. When this is the case, the collective decision-making process going well (or going as it should) is no longer almost exclusively constituted by our doing things that make for decisions that are good. The fully virtuous process is no longer simply the epistemically virtuous process. The suspect reasons, even if they are good, are excluded from our model of good decision-making.
(4) We might imagine other sorts of obligations not to present certain reasons in some context of collective decision-making. These too would count as unacceptability conditions (and support the exclusion of relevant reasons from our model of good decision-making).
(5) Why or under what conditions would such considerations of personal respect rise to this level of importance? Why might one be obligated not to press a reason (out of respect for the beliefs of conscience of one’s fellows) when that reason is crucial to getting an important decision right? Why say that the corresponding ideal decision-procedure is genuinely ideal when the comparative reliability costs are super-high (say the ideal procedure is 51% reliable but there is an alternative “less mutually respectful” procedure that is 80% reliable)? I don’t have any general answers.
(6) Estlund’s version of political liberalism, I take it, would say something like this in response to the above questions: these considerations of personal respect rise to the level of prohibitions on presenting or pressing certain reasons when what we are deciding is the conditions under which we are subject to the collective coercion of the state. I take it that it is not simply the high stakes here that are supposed to do the work, but rather something distinctive to state coercion (or perhaps any sort of inescapable, nearly-impossible-to-resist collective coercion). Maybe the idea is this: given that we are deciding to do things that might limit the agency of each of us in profound ways (and maybe in ways that are unfair, given that the process is fallible), each is owed the respect of not being asked to accept propositions that violate one’s sense what is tolerable relative to one’s vision of how to live life (or one’s “qualified” vision – e.g., the vision might have to not be too crazy or too immoral).
(7) How might these sorts of considerations be relevant to or fit with consent theory? We can imagine our having obligations not to give or press certain reasons on others in the process of coming to or negotiating agreement – this is the most obvious way I would take unacceptability considerations to apply to consent theory. I doubt it, but maybe this is relevant and interesting for developing the theory. But I think Estlund’s account turns on non-consensual coercion by the state being necessary and justified, with the remaining, fraught question being that of how to respect the agency, meaningfulness, dignity, etc. of citizens given that this is so. This is what his acceptability requirements do. So there is a functional-similarity between acceptability conditions and consent as well – both, in the context of their respective theories of legitimacy, would achieve respect for agency and for what makes life meaningful for people in the context of state coercion or enforcement (or something similar in the absence of the state). However, I don’t think it makes much sense to ask “How would acceptability conditions do their work in generating legitimacy if legitimacy is generated via consent?”