There is evidence that liberals have more desire for cognitive complexity compared to conservatives, which can either be framed as a virtue like intelligence or a vice like flip-flopping depending on where you stand (see Jost, Glaser, Kruglanski,and Sulloway 2003). There is also evidence suggesting that extremists on both sides are the least cognitively complex.
I thought I’d examine the time elapsed in taking the Moral Foundations Questionnaire on YourMorals.org and the results are pretty much what you’d expect. Time spent on the questionnaire is lower on the extremes of political liberalism and conservativism. However, liberals did take more time on the page compared to conservatives.Below is a graph of the median time spent on the page by political orientation. The last 3 bars are for libertarians, people who don’t know or are apolitical (strangely, they take the most time on the page…maybe they just have trouble making decisions), and people who are ‘other’.
Of course, it’s up to the reader to determine whether you buy the idea that time elapsed in answering questions about morality is correlated with considering the questions more deeply, which indicates more coginitive complexity in the moral realm. Liberals do score higher on moral relativism measures, which could be thought of as a type of cognitive complexity.