Rather be called a slur

Binarix Lestrange

No binarie el compañere.

EDIT: la compañere? Shit, back to square one.
Le compañere? Maybe. Articles in Spanish are rigidly male or female, the gender sometimes determines the difference between identical words.

El radio: the metal radium / La radio: the radio (AM, FM, shortwave, etc.)
El cometa: the comet / La cometa: the kite

I like binarix, have a dominatrix feeling

Really, if you replace "gender of the person" to "gender of the noun", ChatGPT is correct.

It's people who can be little more picky about pronouns and stuff

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.

's cool

Because what could possibly go wrong by inferring everything based on context?

Turkish has only one third person pronoun that encompasses he/she/it. Gender is similarly indicated with contextual clues.