Two studies show it depends on the topic. One study found complex and nuanced language for topics that differ by party.
"Conservatives exhibited more complex thinking on ... open-door immigration, smoking, castration, and easy access to birth control. Liberals were complex when discussing organized religion, abortion on demand, making racial discrimination illegal, and being assertive".A second study found dogmatism common to both left and right but the topics differed.
The researchers report, "Conservatives are indeed more dogmatic on the religious domain; but liberals are more dogmatic on the environmental domain."