It depends what is meant by the word "sexism", which to the public usually means something like "discrimination based on sex", but to those in the know refers to some putative destructive ideology, or even "absence of sufficiently favorable conditions for women". Hence their use of peculiar monikers such as "reverse sexism" to mean discrimination against men, rather than simply "sexism".

An illustrative example of this attitude is in the UN's Gender Inequality Index, where, in factors in which women are advantaged (such as lifespan), larger gaps push the figure down rather than up (so larger gaps are considered as more "equal" in those areas that already favor women).

Much like racism, sexism appears to only go one way in the mainstream media

I gather you are claiming that there is sexism but in the other direction?

I disagree, strongly.

"female Ph.D.s are disproportionately less likely to apply for tenure-track positions, yet when they do they are more likely to be hired"

These two statements are strongly connected. Women with equivalent qualifications are not applying for the same jobs that men are.

I suggest this is because female candidates are self-selecting themselves out of positions they are less suitable for, but equivalent male candidates are applying anyway.

As such, male candidates must be selected out by the hiring committee instead (where they will contribute even more to these statistics by applying elsewhere).

It's not evident to me that women are being treated equally here, even leaving aside their disadvantage from historical sexist practices.