“relative truth” can mean different things, and people sometimes confuse them (at times even intentionally).
On the one hand, we have become more sophisticated in how we talk about our ideas. Fundamentalists would call one of the model "absolute truth." But folks who have learned from the enlightenment understand it as a human description (the common word is “model”

of something God did. We understand that Scripture uses many ways to describe it, and that the models each capture only part of what Scripture says, and thus presumably what God actually intended. That means that “postmodern” theology is much less willing to pick one of the models and say that it’s simply the Biblical view of the atonement. Is this relative truth? In one sense yes. It’s certainly a modern / postmodern approach to truth of this kind. (I don't want to imply the medieval theologians were completely uncritical. In some ways fundamentalists seem to be trying to restore an approach that was probably never really there.)
On the other hand, we have the idea that all religions are “equally true.” This is probably what most people mean when they talk about losing “absolute truth.” You could, of course, view religions much like the models of the atonement, and say that none of them captures fully the nature of the absolute.
But there’s a difference between the two cases. First, with models of the atonement, the major models can all be connected with descriptions in Scripture. Few theologians would say that every possible model is equally good. You can look at how well a model incorporates its evidence. You can also say that some seem more central to the way Scripture talks about Christ, and that some don’t really do justice to any significant data. By and large the models don’t contradict each other.
You could in principle do the same with religions. But the people who say that all religions are equally good are not normally looking at evidence to assess which religious approaches might do justice to more of the evidence than others, nor do they seem to be noting that many of the views contradict each other in pretty fundamental ways.
I don’t think we can or should ever return to naive views of truth (not that the better Christian thinkers were ever as clueless as many portray them). We’re stuck with critical thought, and it’s a good thing. That may well mean that we don’t really think any human expression of a major truth is absolute -- and this includes Scripture. But critical thought has to be deployed intelligently. Emergent is vague enough that I'm not willing to make absolute statements about it. But the emergent writers I'm familiar with seem to use critical thought reasonably.