I have experience women's public bathrooms before.
The only case where I have seen people who have crap*ed in the sink was a woman's bathroom. Same with the trash can. both men and women on the floor. Tampons, used of course, all over the place stuck in strange places. 90% of the feces stuck on walls on mirrors, etc was in a woman's restroom.
I can not explain it.
The worst case ever was just after I clean the restrooms, (it was the 1st job right after I moved east), I knew they were clean. A classy woman in a expensive car came in and proceeded to mist 2 walls of the restroom in brown. I have no idea what she did or had, but it was gross. I refused to clean it after that.