During the talk I had with Milla the other day, I started thinking about what gender would be like without the binary. And before I go on- let me make something clear. When I say "without the binary" I do NOT mean "without wermen and women", I mean "without the idea that everyone must be either a werman or a woman. Not both, not neither. One. Or. The. Other." (as well as the cissexist binary which says "and what you are is based on your genitalia" and "breaking gender roles makes it okay to mistreat you").
The vast majority of cultures I know about (aka. USA, UK, some of Europe) go by the cissexist binary. Pretty much everyone is raised in it. There are almost no androgynous characters in books, movies, TV shows, or anywhere else. Androgyny in real life is met with confusion and disgust. In other words- the binary is so heavily ingrained in everything around us, it's bound to effect how we see gender. I don't know how much a person would have to do to completely detangle the ideas of gender that've been internalized over the course of our life. If even a 3 year old can have so heavily internalized the that you have to remove your penis to be able to be a girl, imagine how heavily embedded the ideas are on someone who's bought into the cis binary for 18 or even 80 years. (and, of course, that's not a criticism of trans people who need to transition to be happy. That would be a bit hypocritical.) Even how I think of gender has been (and still is) heavily influenced by the cis binary.
I fully believe that, if we ended up completely getting rid of gender- medical transition would still exist (it might even be more prevalent because there's no gender-based reason to discriminate against it) because bodily dysphoria would still exist. But even if we didn't get rid of gender, and just got rid of the toxic form of the cissexist binary that's imposed on us from a birth, what would gender be like? How would people think about gender if they weren't raised with rigid roles and truly given the freedom to make their own choice when they're ready? Even in cases like Pop, the binary is still all around us. Even if a child isn't raised being taught their place- it won't be long until they get inundated with it by playmates, the media, strangers on the street, even friends and relatives.
I don't really know, obviously. I think gender would still exist, but maybe in a very different way. It'd be interesting to find out- but I doubt I'll ever see it happen.