Obamacare provided healthcare to hundreds of thousands of people in coal country, many of whom never had it before. How did that go over again? Let's not pretend Democrats do nothing for the poor and spend all their time drafting hate crime laws for transgender feminists. The reason these voters switched was because they began to prioritize social/religious/cultural issues. However, the socially conservative populist voting bloc that used to be so influential is rapidly diminishing, being replaced with generic right wingers who have bought into the GOP's economic agenda as well.
I don't pretend that at all, what I'm suggesting is that the Democratic platform, even if implemented fully, probably wouldn't be enough to tackle the endemic poverty in many Appalachian locations. And yes, it's obvious that the GOP has been taken over by a not-so-fresh blend of evangelicals and Tea Partiers who accept trickle-down economics as sacred and proclaim government regulation of markets as an affront to God's plan. It's only natural that the philosophy would have to be branded in a certain way to make it more palatable. Subsidized health insurance isn't completely free, either, and many of these people prioritize their short-term financial interest above all else, so until we provide them with the infrastructure for new skills and jobs, the situation is not going to substantially improve.
In sum, do I think these people would be better served by voting Democratic? Yes. Do I blame them for thinking otherwise? Not really. Hypothetically, you have two sources of income for your household; one income from a coal plant job and one person on disability assistance (this would even be an improvement over some families' current conditions). The Democrats attack environmentally harmful energy practices; the coal plant shuts down, maybe "because of Obamacare." Whatever the actual situation might be, it's not hard to see how someone could come to the conclusion that the Democrats aren't working to protect their interests.
It's also helpful to bear in mind that many of them just stopped voting, and the turnout in these areas was never good in the first place.