For my object I tried to think of something used equally by both genders. Everyone sits down, everyone uses chairs. By this logic a chair is absolutely gender-neutral.
Upon further investigation, a desk chair is more than that. This isn’t a chair you would necessarily find in any cubicle as the comfort is at least above average. I picture a chair of this design (although likely much more expensive) in the office of a high-ranking person. CEOs and other high-ranking business people are traditionally men. When you look at it this way, the chair is masculine.
On the other hand, a comfortable desk chair has some traits we commonly categorize as feminine. The cushion has more curves and is gentler. It’s something used to seek comfort over standing or sitting on the ground. It’s flexible, not stubborn (it leans back and spins). By this logic, the chair is feminine. Really it is all a matter of perspective.
When I encounter someone who is androgynous in person I often feel slightly uncomfortable. This stems from the initial confusion, but more importantly from what I should call them. Calling a woman “sir” or a man “ma’am” is pretty embarrassing and might make them feel bad about their appearance.
One distinct example I can remember is when me and one of my friends were serving people at a benefit meal in high school. My friend Ryan served this kid in a t-ball outfit (with a hat on) and said, “Here you go buddy.” The grandfather plainly says something to the effect of “that’s a girl.” My friend felt really awkward. However, what was more bothersome to me was that the grandfather was reinforcing traditional gender roles by being offended, while simultaneously expecting us to not assume a kid wearing a t-ball uniform is a boy.