Mostly unconcerned about appearance and manners, biographers suggest she focused on her studies. A distinguished algebraist Olga Taussky-Todd described a luncheon, during which Noether, wholly engrossed in a discussion of mathematics, "gesticulated wildly" as she ate and "spilled her food constantly and wiped it off from her dress, completely unperturbed". Appearance-conscious students cringed as she retrieved the handkerchief from her blouse and ignored the increasing disarray of her hair during a lecture. Two female students once approached her during a break in a two-hour class to express their concern, but they were unable to break through the energetic mathematics discussion she was having with other students.
From a comment at Dalrock:
Famously, the mathematician Edmund Landau was asked if Noether was an instance of a great female mathematician and he replied humorously – “I can testify that Emmy is a great mathematician, but that she is female, I cannot swear.”
If men with the talent have found positions and there are still resources for a female mathematician on a university faculty, perhaps she could just give lectures without exercising a role of authority over male students. Or she could focus primarily on research/scholarship, under the headship of the men who are there. (As it is unlikely she would marry.) Or she could teach female students.
Creative Mathematical Genius