There could be a bunch of reasons. Republicans tend to live in rural counties, republicans are less likely to trust doctors, republicans are further from hospitals, or democrats are more likely to afford healthcare and accept public assistance.
Or it could be completely irrelevant. Who knows? (Note: Looks like the article authors controlled for the distance from hospitals)
Not over a year but over decades I expect many indirect consequences of policies - like an underfunded energy grid fails and you cannot get your heart attack treatment timely... like a butterfly effect, not immediately visible but snowballing over years in the statistics.
I am skeptical, because almost all of the effect was due to white populations in republican counties (as they point out in the article). Other ethnicities apparently performed similarly across counties (again, as they point out). Seems a lot more likely that the decline of racism over the recent decades has just made poor white people look like poor other ethnicities (which we do see in the data). This also correlates with switching to vote Republican because you tend to vote populist when you are getting screwed and the Republicans have been the party of populism for at least the last decade. Anyways, the point is this study should be viewed with extreme skepticism because it is doubtful they captured all the external confounding factors.
Or it could be completely irrelevant. Who knows? (Note: Looks like the article authors controlled for the distance from hospitals)