Comparisons of these two maps make startlingly obvious the extent to which population density predicts voter behavior. Though not a perfect match, the relationship is undeniable -- and ultimately enigmatic.
The relationship is definitely there. I've seen another map where the population is shown as a 3d bar graph coming out of the locations, with red vs. blue counties.
The statistician's perennial caveat is that "correlation is not causation." but there is little doubt that there is connection, largely unexplained, between ideology and demography.
One thing I noted throughout this article though, is that the question of causation which way was never asked. Are people in low population density areas then influenced to become Republican? Or do Republicans tend to move towards low density areas? The first seems to be assumed in the article, but the second seems quite likely to me as well. Republicans are seen as the party of small government, generally favored by the "leave me alone" sorts. Those same sorts are the type that would tend to like some elbow room, and would prefer to live in low population density areas.