“Indeed literalist-fundamentalism and the critical approaches to the Bible are but two sides of the same coin, insofar as each assumes that the text should be accessible to anyone without the necessary mediation by the church.”
-Stanley Hauerwas, Unleashing the Scripture
The Via Media has many detractors, which is kind of funny because there isn’t much of a definition. As Evan Rohrs-Dodge has pointed out, it is more of a hermeneutic than a monolithic perspective. Joel Watts has helpfully differentiated between the Via Media and the Third Way; at its best, the Via Media is not so much about picking the “middle” between existing options, but about emphatically refusing both and choosing something different.
This shows up in how we approach Scripture. Both conservatives and progressives approach the text in quite similar ways. The fundamentalist-modernist split of the early 20th century was not, as is often advertised, a divide between moderns and anti-moderns, but between different types of modernists who were ultimately kissing cousins. Hauerwas, in his firecracker of a book on Scripture, puts it this way:
“…the debate between fundamentalists and biblical critics is really more a debate between friends who share many of the same assumptions. The most prominent shared assumption is that the interpretation of the biblical texts is not a political process involving questions of power and authority. By privileging the individual interpreter, who is thought capable of discerning the meaning of the text apart form the consideration of the good ends of a community, fundamentalists and biblical critics make the Church incidental.” (25-26, emphasis added)
In today’s UMC, the church is indeed incidental to how traditionalists and liberals read Scripture. Both affirm the church insofar as it affirms their reading of Scripture, and reject the church insofar as it rejects their reading. The individual interpreter – and their respective camps – is king. True heirs of the Reformation, we Methodists are happy to each be our own Luthers, declaring our sole ability to take a stand on Scripture and close our ears to all other readings. The shared attitude of liberals and traditionalists is thus: power and authority are ‘mine,’ and the church only deserves either if and when she agrees with me.
This Enlightenment focus on the rational individual means that fundamentalists and modern critics are really allies. As Walter Brueggemann tells it, this 18th century “text” dominates (however covertly) the reading of those who consider themselves opposites:
“The power of this text shows up  in an excessive theological conservatism that has transposed fidelity into certitudes that are absolutes about morality as about theology, as though somewhere there are rational formulations that will powerfully veto the human ambiguities so palpable among us. The power of this text also shows up  in overstated theological liberalism in which every woman and every man is one’s own pope, in which autonomous freedom becomes a fetish and all notions of communal accountability evaporate into a polite but innocuous mantra of “each to her or his own.” (5, emphasis added)
In other words: conservatives have no room for ambiguity, and progressives have no room for accountability, and both have a poverty of hospitality because of shared assumptions about how to properly read the Biblical text. That sounds to me like exactly where the UMC is at present. The Via Media rejects both of these individualistic, modern readings of the Bible because both are fundamentally modern (pun intended).
What is the alternative? That is a whole separate post, and probably more than one. A hint: something like a Barthian reading of Scripture, or a narrative reading. I would suggest a view of Scripture that takes the text seriously, but short of bibliolatry and far away from demythologizing. The Bible is not merely a list of rules or an outmoded, ancient list of rules (see: literalist and modernist readings) but a story. That story is the narrative of a God known through the travails of Israel and the Church, and most particularly through the life, ministry, death, and resurrection of Jesus. A focus on the person and work of Christ as the primary hermeneutic lens through which to read Scripture thus upends the Pharisees on the left and the right, for whom the only lens is The Agenda. The teaching and the way of Christ are best determined and lived out in the community of faith, the Church.
Hauerwas and Brueggemann give us ammunition for just such a rejection of the twin options of modernist Biblical interpretation. The Via Media refuses to do an end-run around the Church, but bears with her, warts and fights and pitiful controversies and all, daring to listen to the discernment of the church catholic (small-c). The resulting conversation is much more interesting than the alternatives.