Much has been written already (and ably collected by Juan Non-Volokh of The Volokh Conspiracy) on David Brooks's NYT column on the problems of conservatives and libertarians in academia. But two important points have been omitted:
First, many have noted that the problem of political barriers is greater in the humanities and, they might add, the softer social sciences. The usual assumption is that this is because of less rigorous fields have greater room for non-scholarly considerations. That may be true, but supply and demand also play an important role.
When I was in college, my professors advised me against pursuing an academic career, despite my excellent record. They knew nothing of my politics. They knew only that there were no jobs for English Ph.D.s. That was 20 years ago, but the humanities job market hasn't improved much. When supply vastly swamps demand, you get lower wages (all those adjuncts) and, when wages are sticky, you also get non-pecuniary rationing. If a department has hundreds of applicants to choose from, its members will choose the candidate they feel most comfortable with. Humanities departments have those kinds of applicant/job ratios; economics departments and business schools, which face competition from both private sector employers and non-academic government jobs, do not.
Second, it's true that conservatives may be drawn to fields like diplomatic history that are out of fashion. But it's not much easier finding a job if you're a feminist literary critic or material-culture scholar with a libertarian, rather than leftist, view of contracts, consumption, and consent. (As far as I know, there are no conservatives doing such work.) A diplomatic historian can cover some courses no one else wants to teach and otherwise be ignored. But if you're engaging the same questions as your leftist colleagues, you're a lot more likely to make them profoundly uncomfortable.