From what I've been able to glean from advocates, modern theology consists primarily of interpreting religious belief in general and scripture in particular as literature, rather than as establishing factual truth.
The interpretation of religion in specifically literary terms avoids many of the most obvious problems with both religion and scripture. As literature, the factual truth of specific assertions — the resurrection, the virgin birth, even the actual existence of God — become no more relevant to the value of the work than that the lack of factual accuracy of any work of literary fiction. It really doesn't matter at all whether there really was a Hamlet, or a MacBeth, or a Scarlett O'Hara. The purpose of literature is to discuss universal truths, not specific facts. Since universal truths hold even in counterfactual circumstances, the explicit fictionality of literature serves to highlight the universal truths.
A literary interpretation of specifically religious belief, however, presents profound philosophical problems, problems so severe that we must consider literature and religion to be mutually exclusive. The adoption of literary interpretation precludes any sort of religious interpretation.
(A religion with no scripture obviously cannot employ a literary interpretation; there's nothing to interpret. Such gnostic religions have their own problems: How do I determine that your supposed gnosis is correct and mine mistaken? If all gnosis is equally "valid", then so is mine that notions about god are just nonsense, and we're at best in the realm of pure opinion, not religion.)
The first problem is that religious scripture is, on aesthetic characteristics, generally not very good literature. The Christian Bible, for instance, is at best uneven: even Homer nods, but Jehovah seems positively narcoleptic. The parts that do have some literary merit (such as Mark) often require specialized aesthetic tastes.
There's the problem of translation, which always compromises literary, especially aesthetic merit, often fatally. Indeed many Muslims assert that translating the Koran utterly destroys its value as scripture. (Arabic evolves like every other language; we might say that it's equally illegitimate to translate the Koran from 7th to to 21st century Arabic, a process which has led to amusing problems such as the ambiguity between raisins and virgins and the more serious issue of vowel markings.)
More generally, the value of any work of literature depends critically on the subjective aesthetic values of the reader. A religion as a religion has to somehow privilege its scripture, but a privilege that can be legitimately denied on subjective grounds is no privilege at all.
But there's a more compelling critique.
Literature is about universal truths, but no work of literature, however compelling, can ever establish a universal truth, precisely because its factual accuracy is explicitly denied. Factually accurate writing can establish universals: no matter what you, the reader, happen to believe about universal truths of human nature, real people really did things, and if their actions contradict your notions of universal truth, so much the worse for your notions.
But a work of literature must reference the universal truths the reader already believes. The greatest works of literature can draw out and highlight the reader's deep and subtle beliefs, but it can never put those beliefs in the reader's mind. For a reader to acknowledge the greatness of a work of literature, she must say, "Yes, I can believe that people really would act that way." Something in the work must "resonate" with something already present in the reader.
Someone who says, "I am a 'Christian' because the words of the Bible resonate with something already within me," has not been fundamentally transformed by the Bible. He has adopted a label and perhaps clarified his existing beliefs, but he has not been transformed. He is fundamentally no more (or less) a Christian after reading the Bible than he was before.
For a person to be truly transformed at a fundamental level, he has to abandon and replace — not merely clarify — his fundamental beliefs. But to do that, one must be convinced not by a "resonance" with pre-existing beliefs but by the actual, factual truth of what he reads. But to adopt a literary mode of interpretation, we must specifically reject that the factual truth is of any more moment than it is for any other work of fictional literature. To adopt a literary interpretation necessarily entails that one abandon the idea of religion as fundamentally transformative: that is to abandon the idea of religion as religion.
The details are unimportant: the literary interpretation of religion must necessarily try to have its cake and eat it too: The literary interpretation denies factual truthfulness when affirmation is embarrassing or ridiculous, and then conflates the resonance with existing human beliefs with the external establishment of universal truth.