I know zero about Taylor Branch, let alone his theology. I agree with Justin Taylor he does get to the heart of the problem of liberal theology in his book Parting the Waters.
Most of the advanced schools of theology, feeling less adequate in a time of science’s empirical miracles and permanent, mathematical truths, protected themselves with scaled-down promises and vague imitations of the scientific method. . . .
Theology, which had once ruled all science as well as all being, was resorting to more and more elaborate shrugs, (pg. 91).
Liberal theology by and large really has nothing to offer which is why many churches that embrace it are bleeding members and are dying (both figuratively and literally).