Sex, gender, and gender expression are different things.

You mentioned intersex conditions at the beginning talking about primary/secondary characteristics being skewed. Usually things like that are fixed at birth (yes, against the will of an infant who doesn't know better and yes on the advice of a medical doctor who probably knows best regardless of what people say), intersex can have lots of different things divergent from standard male or female genotypes. Hormones, genitals, that kind of thing are all to do with how you developed in the womb, physically. Those things are related to physical sex.

Gender is how you identify. This is where I lose it a little bit. Being trans myself, I know what it's like to not match your physical sex, and it sucks. But it's a legitimate thing, backed up by science. It's not a mental disorder, and most trans people who transition do it to ease their Dysphoria. Again, all based in science and modern medicine agrees with this.

Expression is basically how you present yourself. So you get, for example, a tomboy who is a girl who presents more masculine than feminine. This has nothing to do with gender and basically boils down to clothing and hobbies.

But things like gender neutral, agender, bigender, I dunno. That shit confuses me from a scientific standpoint. People are hard wired to be male or female in their brains (lots of research on this), and it doesn't make sense to me. Peoples bodies have to have hormones of one type or another, otherwise it can lead to shit like osteoporosis. To have your brain hard wired for both genders, or neither, I'd need to see some proper research to accept it.

I know that hypocritical as a trans person, but I'm just not convinced that neutral gender exists, I don't see how you can be fluid on a gender level (expression yes, but not in your mind), I just don't get it.

TL;DR: Some gender stuff makes sense and is scientifically proven, but special snowflake stuff doesn't track with me.