The reason that so many conservative evangelicals these days appear to be moral relativists is that they *are* moral relativists.
They would deny this, of course. But that doesn’t make it any less true. Here's why.
They’ve bought into the premise that all statements are either fact or opinion: facts are objective and verifiable; and everything else is opinion—subjective and unverifiable. In other words, they've bought into full-fledged modernism.
From there, the secular path to moral relativism places all moral statements in the “opinion” category. On this view, morality is subjective—dependent on cultural context, historical background and the like.
Conservative evangelicals recoil from this approach, as they should.
So instead, they place morality in the “fact” category, claiming that moral truth is objective and empirically verifiable.
And how is moral truth empirically verified? The Bible, of course. Problem solved.
This is tempting, for two reasons. First, Scripture is entirely true; and much of that truth pertains to morality.
Second, apart from special revelation, it’s difficult to imagine where we might go to find empirical verification of moral truth—you can't *see* moral properties.