Where are all the conservative university professors?" This is a perennially interesting question, enough so that I got into an interesting FB conversation about it with a friend. On the off chance that anybody else could benefit from my side of that conversation, I'm going to reproduce my thoughts here.
In case you don't want to click the link above and read the attached article, here's a basic summary. What the author is looking at more specifically is why there aren't self-identified conservatives (or very many) on the faculties in humanities and social sciences departments. The article acknowledges that business and engineering are different animals, but since a lot of people equate "college education" with some pieces of the liberal arts, the question of how "liberal" they are is a relevant one, at least in the public mind.
I should stop and point out that there are real political scientists who have studied this question with actual data. You can find one of the better examples of this at this link; the research is written by a couple of friends of mine who are genuinely interested for scholarly, as opposed to op-ed, reasons. The article linked at the top of this post doesn't really get into data; it's more about rampant speculation.
That speculation boils down to this: current incentives for humanities and social science professors involve doing research that questions existing conventional wisdom, often in radical and new ways. This is means by which these disciplines advance knowledge, and it's also the path to success for professors who must "publish or perish". Because questioning things from radically new points of view and trashing conventional wisdom are seen as liberal, not conservative, traits it stands to reason that professors in these fields will likely be more liberal than conservative.
This is a plausible explanation, but only barely. I think there's some element of truth here. It is the case that "boundary-pushing" research in the humanities and social sciences encourages questioning things that are political and normative in nature. Similar cutting-edge research in engineering or medicine doesn't generally call into question preexisting social and political beliefs. Business is built on a set of assumptions which are fundamentally conservative (in the classic sense) to begin with, and so research within that paradigm is likewise unthreatening to conservative views. So it is reasonable to observe that there would be more political bias or impact in fields in which the subject is more inherently political and philosophical in nature. There is no such thing as "liberal engineering" or "conservative engineering" - there's just engineering, because designing circuits or aircraft isn't an ideological exercise. Interpreting Shakespeare, studying and analyzing history, and researching sociological phenomena all involve political & ideological issues.
All of this is only true if you understand "conservative" to mean what Edmund Burke meant: a respect for tradition and the past and a desire for change that is evolutionary and measured rather than radical. In this regard, modern humanist scholarship is indeed "non-conservative" in that it tends to reject what has come before and want to start fresh, rather than preserving and respecting inherited wisdom. By this standard, many who call themselves "conservatives" today aren't conservatives at all, which further muddies the waters.
I think the much better explanation for the original question - why so few conservative faculty in the liberal arts - is basic tribalism. People tend to sort themselves - where they live, what they do for a living, who they interact with - into groups that are comfortable. The fact that some (many?) humanities and social sciences departments ARE deeply liberal tends to drive conservatives away from those fields, because it's just not comfortable to be there. This is a complex phenomenon with a number of different vectors, as my colleagues who study this stuff will undoubtedly point out. But I wonder whether it doesn't have more to do with our social relations than with the nature of what we study as academics.