Linker's "illiberal" liberal state

Linker's liberalism (a view of liberalism shared by Dwyer, Ackerman, and others) requires religious believers to accept what he calls the "liberal bargain," which, in practical terms "means that your belief in what the Roman Catholic Church believes and teaches is irrelevant, politically speaking."

Does Linker's liberalism excommunicate (disenfranchise) Catholics (and other religious adherents) from the political community?  I'd be interested in hearing the thoughts of other MOJers and our readers on this question.

My answer to the question is "yes."  I can't dis-integrate my core beliefs about human nature, society, history, etc. from my life as a participant in the public sphere.  And, even if I could, I would be unwilling to do so.