A more fundamental issue is that conservatives tend to be skeptics about the progressive epistemology that defines the modern university. According to this vision, the goal is to “discover new knowledge”. As a result, research is treated as more important than teaching, and teaching is understood as an assault on prejudice rather than the continuation of tradition.
This conception of the academic enterprise makes it tough to get through grad school if you see teaching as your main work or are inclined toward curatorial forms of scholarship (even though research is a relatively small element of most academic positions). Conservative social scientists may have fewer objections to this bias toward novelty. But it’s a real challenge for conservatives in the humanities.