Protective Duties and Bounties
An early passage from Mill's The Subjection of Women suggests a potential tension between Mill and (some) modern feminists:
What women by nature cannot do, it is quite superfluous to forbid them from doing. What they can do, but not so well as the men who are their competitors, competition suffices to exclude them from; since nobody asks for protective duties and bounties in favor of women; it is only asked that the present bounties and protective duties in favor of men should be recalled.
If only it were that simple! In some areas, such as voting rights, it appears to have been sufficient to just make the laws equal, and women could exercise their rights with full force. Yet in so many other areas, it seems that more affirmative action (to use that phrase in a broad context) has been necessary. This would seem to be in tension with Mill's analysis.
It is hard to tell if Mill's mistake, if he is in fact making one, comes from underestimating the lingering effects of such a long tradition of gender subordination, or from overestimating the self-corrective power of market forces. Or perhaps Mill would eliminate the tension with line-drawing. As a quick example shows, it is not always clear whether a particular policy argument involves enacting "protective duties and bounties in favor of women" or simply eliminating "present bounties and protective duties in favor of men."
To the extent that a police department's height and weight restrictions are simply traditional proxies for fitness, doing away with them might very well fit into the "present bounties and protective duties in favor of men" that should be done away with. Mill could thus argue that changing those restrictions, or including a different set for women (like the Army's different physical fitness standards) is simply eliminating status quo preferences for men rather than any concession to assist otherwise uncompetitive women. To the extent, however, that any such restrictions reflect necessary functions of the job, I would think Mill would not favor making exceptions or concessions for women.
In that sense, Mill has perhaps implicitly foreseen, but swept under the carpet, a very complicated set of questions. What are the types of criteria and requirements which really serve as proper assessments of capacity to perform the particular function? And which criteria reflect built-in prejudices for the way a man would do the job, or worse, are mere proxies for discrimination? At the margins, it seems pretty hard to know the difference.