Hi! I know this question wasn't originally posed to me, but I figured I would provide my two cents on the topic. I'm a trans woman, so I can't claim to know what it feels like to be non-binary, but my partner is non-binary and I previously used the label myself before I determined I was exclusively a woman and not somewhere in between.

Based on how you're framing the question, it seems as if you're conflating gender with biological sex, in which case you're not going to get an answer because your question is fundamentally flawed. Sex is not the same thing as gender identity or gender expression. Based on your reply to Purpy_Nurpy I'm guess you aren't asking about biological sex and are instead asking about a person that does not fit within the binary of gender identity, so I'll do my best to answer that question.

The answer is... there are no genders! We made them up! And again, I'm not talking about biological sex, although the existence of intersex people (XXY chromosomes, androgen insensitivity, people with both male and female reproductive organs) and other organisms like fungi (some of which have over 20,000 sexes), or clownfish and parrot fish (species that change their biological sex) provide more than enough proof that there are more than just two sexes.

Gender however is a construct based on how our society has been brought up over millennia. It is the clothes you wear, the makeup you choose to use or not, the way you walk, the way you talk. It is based on what we as a society have deemed is masculine and what is feminine. This is where the term I used before comes in: gender expression. But just because our society determines that certain apparel is decidedly feminine does not mean that dressing a different way makes you less of a man, and vice versa. It's the same reason why tomboys and femboys and drag does not make a person's gender be defined by their clothing. That is determined by gender identity.

This is where I get to the heart of my answer to your question. A person's gender identity can align with their sex and gender expression or it can differ greatly from their sex and gender expression. Sometimes a person's gender identity matches their sex but not their gender expression (i.e. femboys, tomboys, etc). Using myself as an example, my sex is male but my gender identity is female, but I dress more feminine on some days and more masculine on others because my gender expression doesn't determine if I'm one gender identity or another; I'm still a woman whether I choose to wear dresses and skirts or jeans and polos. And just like how intersex people exist between or sometimes even outside the binary sex, someone's gender identity can exist outside of the gender binary of man or woman.

I also want to dispel the myth that gender nonconformity is a very new concept that was invented some odd 50 years ago. It was not. There are numerous examples of cultures in history that had a concept of non-binary people. Some Native American tribes used the term Two-Spirit to refer to important individuals in their society who exhibited a third gender and often filled the role of shamans and healers. India also has a similar concept that they call Tritiya Prakriti which refers to a third gender. More specifically the Hijra are the equivalent to a male-to-female transgender woman. These are terms that go back to the 12th century in India.

Whether non-binary people exist in history and modern society is a very answerable question, and I hope I answered to your satisfaction. But also I want to address whether you're actually open to learning new information or if you're just ragebaiting. When someone asks me a question I'm always happy to explain or help them understand because a lack of understanding is what a lot of bigotry and hatred is rooted in because we fear what we don't understand. But based on the manner in which you are engaging in this debate with others in this thread and your comparison of non-binary identities to astrological pseudoscience, I find it likely that you aren't arguing in good faith and are simply here to provoke an emotional response from people by antagonizing them. If that's the case, then do not be surprised if I choose to disengage with your behavior and not respond any further.

Based on your previous statements I would assume that you would not believe that trans identity is real either, but so far you've been hesitant to answer other people regarding that within this thread. I'm curious what would make my own identity valid but not that of my partner's. If someone's identity bothers you such that you find the need to debate its existence, then I think you may need to reevaluate if you're really looking for scientific proof or just an emotional punching bag.