Richard Ostling has an approving review of a book by two evangelical authors on the nature of truth. These authors juxtaposition two positions. One side holds that truth is what feels good while the other side believes that truth is what corresponds to reality apart from what we "perceive through physical or rational faculties".
The first position is labeled "secular liberalism" or postmodernism while the second position a form of realism. There's a whole range of views of truth which are not covered by either position. And the labels themselves are dubious. What they classify as secular positions are held by many religious folks.
One could argue for gay marriage and hold any number of views on truth, including the one these authors hold. And one may also reject relativism and reject the positions of the authors. Let's look at Emanuel Kant, who was no post modernist. He rejected the idea that truth can be reached apart from our perceptive powers.
Reality is "out there" but it has to be made into something which is understood and presented to human consciousness. This view argues that there is an outside world and yet also recognizes the work we must do to present some of it as an object to us. This view fits neither position these authors put forward.
I think the problem here is that the authors imagine that the differences in culture war issues all break down into "world views" and epistemologies and so that if we can "fix" that, there would not be disagreement. I've never seen why this should be the case and never have seen it argued for, just assumed.