Gross and Fosse have a supply-driven theory of leftist domination of higher education:

A pair of sociologists think they may have an answer: typecasting.
Conjure up the classic image of a humanities or social sciences
professor, the fields where the imbalance is greatest: tweed jacket,
pipe, nerdy, longwinded, secular — and liberal. Even though that may be
an outdated stereotype, it influences younger people’s ideas about what
they want to be when they grow up.

Jobs can be typecast in different ways, said Neil Gross and Ethan Fosse, who undertook the study. For instance, less than 6 percent of nurses
today are men. Discrimination against male candidates may be a factor,
but the primary reason for the disparity is that most people consider
nursing to be a woman’s career, Mr. Gross said.

My colleague Dan Klein’s not buying this.  Non-leftists with Ph.D.s in the humanities and social sciences are still much less likely to be academics:

We found that Republican-voting members of the scholarly
associations were significantly more likely to have landed outside of
academia. For example, in Anthropology/Sociology, 43% of the Republican
scholars were working outside academia, compared with only 24% of
Democrat scholars. In History, it was 47% versus 27%. In all six
disciplines overall, it was 41% versus 25.

The individuals we are talking about here are members of the
American Anthropological Association, the American Historical
Association, and so on. Most had PhDs. So we find that
Republican-voting members of such associations are consistently more
likely to be working outside of academia – in government, private
sector, independent research, or other. Do we think these people don’t
care for research and learning, that they just don’t want the income,
security, prestige, and student attention that professor status
affords? Then why are they members of such associations?

Klein persuasively argues that the nurse analogy falls flat:

Besides, the analogy to male nurses doesn’t ring true for the non-left
professor -classical liberal, libertarian, or conservative, not
moderate or uncommitted. I’ve never dreaded telling an acquaintance I’m
a professor. I don’t fret that he would assume I like FDR or The West Wing or single-payer healthcare. Why should I care if he did? Would a woman
dread reactions to the revelation that she is an elite chess or poker
player—both games dominated by men? More likely such a woman would
feel special pride in having cracked a male field. Many non-left
professors may feel that way. Also, the non-left professor surely has
the comfort of blaming leftist bias for his not being more eminent.

But doesn’t the basic economics of discrimination make non-leftist whining grossly implausible?  Not at all.  As I often remind Alex Tabarrok, the basic economics of discrimination assumes that firms maximize profits.  Since academic departments are essentially non-profit worker coops, widespread discrimination is not just possible, but likely.