Brett Parker has posted this paper finding a moderate increase in ideological polarization on state supreme courts:

Research has documented elite polarization in a variety of areas, including Congress, the executive branch, and the federal judiciary. To my knowledge, however, no work examines whether state high courts have polarized or to what extent. This research fills that gap. I create the largest and most comprehensive existing dataset on state supreme court judge party identification (running from 1980 to 2020), and merge those affiliations with an expansion of the ideology data from Bonica and Woodruff (2015). I measure polarization using two metrics: first, I examine the degree of ideological overlap between Democratic and Republican judges; and second, I track the ideological distance between the Democratic and Republican medians. I also examine whether the various methods of judicial selection are associated with different degrees of polarization. I find a modest increase in polarization across the entire population of state supreme court judges, but they still lag behind other government institutions in that regard. Each selection method I consider is associated with at least some increase in polarization (as measured by either overlap or distance), but no single method stands out as having a particularly close relationship with a polarized judiciary. Finally, I document increased polarization in states with nonpartisan elections as compared to others in the aftermath of the Supreme Court’s decision in Republican Party of Minnesota v. White.