In a recent posting entitled, "An essential Presbyterian conflict: Reformed versus Celtic faith," the Rev. N. Graham Standish argues that one facet of the conflict among Presbyterians today is our dual heritage of a dualistic Reformed-Augustinian theological tradition and a more holistic Celtic spiritual tradition. He writes, "Certainly there are other ways of analyzing the conflicts we have in the PC(USA), but looking at these roots is one way. And if this analysis is true, then we may be in conflict because our Reformed side regards human nature as essentially tainted, while our Celtic side regards human nature as essentially good." He goes on to flesh out the difference between these two traditions: "The more Reformed we are, the more we tend to gravitate towards an Augustinian, fall theology, interpreting Bible through the story of Genesis 3. We embrace the idea that original sin has tainted all of humankind, leaving us depraved and requiring God’s grace to forgive and redeem us...The more Celtic we are, the more we interpret the Bible through Genesis 1, gravitating towards a “goodness” theology grounded in God’s declaration that all in creation are “good. This theology recognizes the power of sin, and the need for grace. But it is tempered by a belief that our natural inclinations are good, and become sinful when gratifying these inclinations turns them into false gods to be appeased. Grace restores us to our natural, essential goodness."
The website, Celtic Christianity Today, contains a page on "Celtic Theological Attitudes," which provides a good orientation to the Celtic tradition. For a longer description of Celtic spirituality see (here).
The extent to which PC(USA) and other American Presbyterian denominations are heirs to Celtic spiritual traditions is not clear to me. A brief article by J. Philip Newell with the title, "Celtic spirituality listens for the heartbeat of God: Presbyterianism is influenced by ancient Celtic and Mediterranean traditions," actually seems to indicate that we have not been influenced by that tradition but should be. It seems more likely that the un-evangelical wing of PC(USA) might become more interested in Celtic spirituality because that spirituality more nearly expresses the temper of our times, which as is becoming less and less dualistic, than because it is a part of our Scottish Presbyterian heritage. In any event, Standish does touch on a central difference and source of conflict between Presbyterians today. On the one hand, those who are leaving the denomination in increasing numbers tend to begin with a generally clear dualistic theology and work toward a consistent spirituality. On the other hand, at least some of those who are staying tend to begin with a less dualistic spirituality and work toward a more inclusive theology.