Here’s another interpretation of how (what Estlund characterizes as) the central thesis of political liberalism might go.
The reasons that favor permission to coerce A but that are not acceptable to A (due to their violating A’s conscience), unlike the other good reasons that favor it being permitted to coerce A, are not part of (they are irrelevant to) one being in a position to make a good case to A that would also be acceptable to A. The screening-off here would not be part of what determines the shape of the relevant good reasoning about the relevant permission to coerce itself, but it would determine the reasons or bits of reasoning (that are part of one’s good reasoning) that factor into meeting the condition that is crucial for the permission to exist (the condition of one at least being in a position to make an acceptable case to A, if not actually making it).
We might think of this condition as like the condition of A granting permission in cases where that is how permission gets generated. The crucial condition is one that concerns respecting the agency and reasoning of A.
This idea has the makings of the right sort of “bridge principle” connecting acceptable and unacceptable reason-giving in discourse about whether P to private reasoning about whether P (for relevant values of ‘P’). Reasons that are unacceptable to A (or that it is unacceptable for one to give A) are reasons irrelevant to one being in a position to make an acceptable case to A. The bridge here is not to good or appropriate reasoning per se but only to defining that part of good or appropriate reasoning that allows one to meet the condition that would generate the permission to coerce A in the relevant context (with respect to government and laws, etc.).
On this picture, we are in an odd position with regard to good but unacceptable reasons that we have favoring it being permitted to coerce A in relevant ways: they favor the relevant permission to coerce, but, at least given the context, they are not part of any set of reasons the having and giving of which bear the special relation to A’s agency and reasoning that generates the permission (and without which permission cannot be generated, at least in the relevant sort of case).
I doubt that this sort of bridge principle – even if we add stuff, as I think we plausibly can, to account for bad/false but acceptable reasons – gives Estlund all that he wants to get or thinks he can get. But I’m not sure.