Gender is grammatical but there are quite a few areas that are defined, if not you birth sex, at least by their prevalence among males or females. Some of these have been greatly diminished by females becoming more prevalent in male gender areas. Occupations, clothing, interests and recreational activities have seen a somewhat diminished male dominance. The reverse, save for an infinitesimal few has not been true. 60 years ago when I graduated 8th grade from a NYC Catholic School we had a Gestetner printed yearbook. Under our names each kid stated their occupational goal. With one notable exception the girls, even the brightest, chose feminine positions, teacher, nurse, secretary. One girl chose lawyer and the nuns tried to have her change. It wasn’t proper. None of the guys chose a feminine gender job, even though I eventually became a teacher. I suspect a yearbook today would look very different for the girls but hardly changed for the guys.
I never had that problem of underestimating potential occupation (I’mm in late 50’s).
I read some doctor who did a sex change operation (I think on a twin boy, due to a botched circumcision) started using gender instead of sex. Both twin boys ended up committed suicide, so not a very good start for using a grammatical word to mean anatomical sex.