Jokes aside, I think the correct one should be "binaria" because it's "persona no-binaria", where "persona" being a female-gendered word still includes everybody (persono doesn't even exist).
Precisely. It is “el género no binario” or “la persona no binaria”. It has nothing to do with the person, just the nouns. As “binario/a” is an adjective, it has no gender on its own.
This legitimately trips up learners. How if the noun is female, it's correct to use feminine articles/pronouns/etc regardless of the person's gender, even if you know they're male. (or vice-versa).
It might be, you know, hear me out, that "grammatical gender" is a historical misnomer caused by linguistics initially practically only looking at Indo-European languages, which tend to have three noun classes with the word for "woman", "man", and "thing" all being in a different category so they became known as feminine, masculine, and neuter, with words assigned to them pseudo-randomly via phonetics. But really noun classes are a much more general thing, Bantu languages have up to 20. Persons, fruits, plants, locations, such things.
At least in Indo-European languages it's mostly about ease of reference: "I see a cup and a table. She is broken". Assuming that cup is female and table male (as in German) that is a very clear and concise statement.
Native speaker here and no, that wouldn't be correct as a general rule. The most typical would be talking about or someone else like "yo soy no binario/a" and "yo" would be a he or a she depending on who is saying that. If you're talking about someone else it's "el/ella es no binario/a" for example.
Also a native speaker here. You can also just not specify "el/Ella" because the context isn't relevant. I.e. "es no binaria". You can also just pluralize the person to get around gendered wording, I.e. "ya llegaron" for "they have arrived" rather than "el/Ella ya llego" for he/she has arrived, but this is informal and may sound odd to someone of a different dialect from me, but I think this should at least be intelligible to Latin american Spanish dialects
Except that in spanish we don't have a gender neutral term so you either explicitly or implicitly have to say el/ella. But yeah, in hindsight it does make sense (semantically) to say "binaria" as if you were referring to them as "personA"