I don’t really see how it could do otherwise. By your argument modernism and postmodernism should accept or tolerate every claim to revealed truth, from the divine despotism of the pharoahs to the idiotic banalities of the new age movement.

Andrew, of course I am not arguing for the naive acceptance of all claims to divine revelation, any more than the Enlightenment naively accepted all truth claims which appealed to rational or empirical justification.  My point is that the whole epistemic category of revelation is itself dismissed with predjudice.  It is laughed out of court.  The real problem isn’t that every claim to divinely mediated knowledge would be embraced, but that ALL such claims are rejected out of hand.

How can a progressive culture avoid putting its epistemic confidence either in empiricism/rationalism or in a radical scepticism? Revelation is almost by definition that which for good reason an intelligent society rejects.

I guess this depends on what you mean by “progressive.”  I might ask the reverse: how can ANY culture progress without taking for granted certain truth claims or assumptions which transcend either rational or emprical justification - not to mention the hopeless, epistemic solipsism of scepticism. 

Really, the problem is ours: What ground do we have for preferring our particular revealed truth over Islam’s or anyone else’s?

As Christians, we have experienced the cross as the power of God, radically altering our lives - turning us from idols to serve the living God.  The believer can say, as Packer remarkably notes in “Knowing God,” I have known God.  Obviously many others outside of Christ can claim this same knowledge, but we have our own experience of the divine, which is immediate, life-transforming, and personally undeniable.  We have experienced in the gospel-proclamation the crucified Messiah of God - which is an affront to the Muslim, a scandal to the Jew, and foolishness to the Greek.  Such a Christ is simply incompatible with Islam, Judaism and the various Gentile religions of power and dominance. 

Of course, there are numerous rational and empirical reasons which can be adduced in support of our faith.  But it’s not so much that rational argument or empirical evidences, as processed through some supposed objective or universally self-evident grid, supports the reality of the crucified Christ, as that the faith which the revelation of God in Christ evinces makes most sense of the rational, emprical, sceptical, and indeed, whole human experience.  As C.S. Lewis said, “I believe in Christianty [Christ crucified] not so much because I see it, but because by it, I see everything else.”  In fact, in light of all this, I might reverse your question again: on what other ground can I possibly stand (cf. John 6:68)?