Postliberal theology is not necessarily Protestant. Fr. Robert Barron is an example of Catholic postliberal theology (his book The Priority of Christ is subtitled Toward a Postliberal Catholicism. I would say, in fact, that postliberalism fits more easily within a Catholic than a Protestant framework. Pope Benedict’s theological work fits the postliberal category fairly well, I think, although I’m not sure he’d use the term. This 1989 article from Chrisis magazine agrees with me on that point.
Perhaps the most important contemporary philosopher on whom postliberal theologians draw is Alasdair MacIntyre. MacIntyre’s book Three Rival Versions of Moral Inquiry lays out the alternatives this way:
The “encyclopedia” model of inquiry, which MacIntyre identifies with the Enlightenment, holds that truth is something objective which can best be attained by a perfectly neutral mind, stripped of all bias and all tradition. Individuals can reason their way to truth on their own, and particular communities, like the Catholic Church, get in the way of the search for truth.
The “genealogy” model of inquiry, which MacIntyre identifies with Friedrich Nietzsche and by extension with postmodern relativists, takes the “encyclopedia” model apart, showing that the supposed “neutral” inquiry of the Enlightenment is really shot through with all kinds of biases. This model, however, can’t be the basis for a stable understanding of truth, because if applied consistently it deconstructs itself. Moral/rational inquiry becomes simply the “debunking” of claims to truth by showing their grubby roots.
Against both of these, MacIntyre advocates what he calls “tradition.” A tradition-based mode of inquiry doesn’t deny truth, but it seeks for truth in conversation with a tradition. Only within a tradition do we have any concept of what are the relevant questions to ask. You can’t get “outside” all traditions and evaluate them neutrally. You can, however, engage in dialogue with other traditions and try to show that your tradition makes sense of the questions their tradition asks. Also, traditions may of course split or merge–they aren’t static entities with impermeable boundaries. (MacIntyre’s big example of a merging of traditions is the way Aquinas combines Augustine and Aristotle.)
It sounds like this theology confirms the verse that scripture amounts to foolishness to non-believers. I like it. It focuses on the culture of Christianity as formed by the language of scripture and doctrine, culminating in traditions. I think this theology is very catholic.