Part of the problem that Professor Bainbridge identifies—one that is far from unique to academia, and that the recent Franken/O'Reilly contretemps reveals all too clearly—comes from a combination of diversity and definitions. "Liberal" is a much more diverse group in this country than "conservative." One illustration in a followup comment to Professor Bainbridge's article demonstrates this more clearly than I might otherwise wish: the identification of certain radical theories (such as Critical Race Theory) as "liberal," even when those theories do not fit with many or most of the other tenets of "liberalism." Those who would treat CRT as "liberal" generally know little or nothing about it, except perhaps what they have gleaned from archconservative attacks upon it by the Ann Coulters of the academic world. And they do exist, regardless of ideology; unfortunately, intellectual honesty appears to have lost weight in the hiring process since the 1960s, both inside and outside academia.
In any event, this is not to say that all conservatives are alike, but only that the views of various flavors of conservatives are more compatible than those of various flavors of liberals. For example, both Marxists and Critical Race Theorists are generally classified as "liberals," but in fact their views are incompatible with both each other and with much of the core of "liberalism"—especially "liberalism" as defined by finger-pointing from the right at anything that some of the more extreme rightists disagree with. (That true Marxists are mostly "social conservatives" seems to have escaped most notice, in any event.) I am reminded of Swift's "The Battle of the Books" by the sniping between the "academic left" and the "academic right" much more than makes me comfortable.
One might also wonder, however, whether the "anticonservative bias" in academia has a counterpart in the "antiliberal bias" in "private industry." For all of the reputation of, say, the ABA as a "liberal" institution, the views of the membership and leadership—as reflected in its actions, such as refusal to make pro bono publico a requirement for lawyers and refusal to take steps to apply ethics rules equally to small-firm plaintiffs' lawyers and large-firm insurance-defense counsel—are far from "liberal." Presuming, again, that there even is such a thing as a single, coherent definition of any broad political class, one could speculate that there is a conscious or unconscious effort in the academy to provide an alternative for "liberals" who don't fit well in the "conservative" business world. And so on.
In the end, this is all navel-gazing, because there really is no single, coherent definition of "liberal," any more than there is a single, coherent definition of "conservative." The fight more often appears to be over the degree of literal textualism espoused than anything else. Right now, the most literal textualists are often identified with "conservatism." That has been different, and it will be different, at other times in the future. We need only remember "three-fifths of all others" to see some of the problems.