At first, this was a term I coined for people who were shocked by the contents of this article, as if the Catholic Church hadn't figured out sometime in the fourth century that not everything affirmed by the authors of Scripture, even taking into account variations of genre and all that, is true.
But then I noticed a pattern: those people tend to be the same ones who subscribe to the Chicago Statement on Biblical Inerrancy. So now I have a clearer definition: "fundie hick" = someone who subscribes to the Chicago Statement. I recommend that Catholics don't even bother with anti-Catholics who subscribe to the Statement, since they will be entirely beyond reasonable discussion. Same goes for so-called Evangelical "scholars;" theology based on the Chicago Statement is pseudo-scientific opinion in the guise of scholarly discipline. Well-educated nuts are still nuts. If they can't conform their belief to some reasonable standard of Biblical inerrancy, like Dei Verbum or The Interpretation of the Bible within the Church, don't bother with them. Conversely, when you see the term "fundamentalism" used in Catholic documents, these are the people they mean.
It seems pretty obvious from the guidance of Pope Benedict and his predecessor, Pope John Paul the Great, that such methods are an insult to the dignity of the Sacred Scripture. With that being the case, I do not see how Catholics can responsibly engage in dialogue within a framework that concedes the legitimacy of such views. The danger is manifested in the blasphemous, anti-Trinitarian views of such authors as John Frame, Vern Poythress, D.A. Carson, Gerald Bray, Paul Helm, and Kevin Vanhoozer (not to mention earlier authors like B.B. Warfield). Having read a good deal of their tripe, I urge people as a prophylactic measure to immerse themselves in the wisdom of the Fathers, who would have never countenanced such absurd anthropocentrism as the Chicago Statement endorses.