Do the studies offer explanations as to why red states have higher infection rates than blue states despite being less densly populated?

With just a few examples in blue states where the virus took hold early on in dense urban areas in blue states, i can't think of any explanation except that red states were much less vigilant with lockdowns.

Testing is a bit of a mess. There aren't any standards and it's highly subjective and interpretative. Some facilities/tests don't even report the CT of the PCR, rendering the result essentially meaningless (which in many cases then also affects death figures, along with the "died with / died of" debacle).

Cherry-picking of course makes this worse - introducing arbitrary and potentially contaminating boundaries such as governmental policy (red vs blue). Did red states generally employ higher CT's? Do we even have that data? No, sometimes its discretionary or not even recorded. We do know Trump was heavily encouraging more testing, as this painted a better (and, to his credit, ever more accurate) picture of mortality rate, so even just that may plausibly explain such a result.

Conversely, at least regarding all of the testing data as mixed establishes a better starting point for analysis less subject to such foibles.