I think that as a policy matter (what interviewers should do or should even be allowed to do), a stronger claim can be made. Suppose there are some groups A1 and A2 (men vs women, different races, etc — there could be A3, etc). Then I would argue that, regardless of whether the groups have substantial differences affecting qualification for the job, group membership or perceived group membership should not be allowed as a substitute for individual qualification. So, as an extreme example, if a job requires heavy lifting and short or contained hair, then an applicant should not be preferred because they’re male.

Obviously there are nuances here. If the groups are actually job qualifications (hiring a singer based on vocal range, for example), then none of this applies. There are surely plenty of gray areas, too. Gender doesn’t fit cleanly into a pair of groups. Sometimes it might be very hard to measure actual aptitude, and proxies of various quality are needed. College admissions are an example of the latter — you can’t measure how well someone can do, so admissions departments use proxies of varying quality and social acceptability.

As for gender differences, if I’m hiring someone, I believe that it doesn’t matter whether one gender is likely to be more qualified for any reason — if I’m hiring, I have an obligation to consider the applicant as an individual regardless of gender.