Third-person singular androgynous, Third-person singular ambivalent

Friday, a co-teacher and I gave a demo class. At least ten parents attended, mostly mothers. The lesson title was "who is she?" In one activity, two students started at opposite ends of a row of picture cards and made sentences using gendered pronouns.
Examples: He is my grandfather. She is my sister.

I designed this activity specifically to address Korean speakers' tendency to refer to everyone as "she," which can baffle, amuse or even enrage English speakers.

I felt hypocritical emphasizing the importance of using appropriate gendered pronouns since: (1) I do not believe in a rigid gender binary; (2) I personally identify somewhere between masculine and feminine.

Also, my teaching this grammar point was ironic since at least some of my students do not believe that I am female. I've heard them asking my co-teachers (in Korean) and audibly disbelieving the answer. For that matter, Korean adults have asked me point-blank whether I was male or female. One older woman in a bank even tried to touch my breast to check for herself.

Later that day, I needed to use the restroom and approached a public women's restroom. A female custodian said (in Korean), "No! The MEN'S room is over there." I shrugged and used the men's room. (Note: I was wearing tan khaki pants, a blue button-down shirt, and sparkly blue nail polish at the time.)

Honestly, I wish I could avoid gender altogether. That's not possible, especially in Korea. Women and girls are much girlier here than they are in the U.S. They wear lots of make-up, climb mountains in stiletto heels, and cover their mouths when they laugh. One does encounter butch-looking girls now and then, however. I wonder what kind of feedback they get about their gender performance.