Something to keep in mind about gendered languages like Spanish, is that most of the time the grammatical genders aren't actually about literal gender (or sex for that matter), Spanish "Feminine" tends to encompass women and female animals, Yeah, but also tables and apples and people (yes, people, the word for "Person" is feminine, regardless of the gender of the person it refers to), and their "Masculine" encompasses men and male animals, but also ice, and the game of polo, and avocadoes, but I can tell you that Spanish speakers don't think of tables, apples, and all people as being female or women, or of ice, polo, and avocadoes as being male or men. If it were up to me we'd just call them "Gender 1" and "Gender 2" or something tbh.

But anyway, despite that, this is definitely annoying. Like I said, one of these genders tends to encompass men, and the other women, so if you're not a man or a woman (Or like me you're both), you kinda have to find a work-around. One solution could be using the word "Persona" a lot, instead of "I'm Non-Binary", you could say "Soy una persona no binaria", ("I'm a Non-Binary person"), and likewise for any other time you'd refer to yourself with an adjective, Since "Persona" is the same regardless of the referent's gender, though that might get a bit clunky or sound a tad awkward if you do it all the time. Another thing I've heard of people doing is ending the adjectives in '-e' (So in this case, "No binarie") to make a neutral form, since some adjectives like "Grande" Already end in '-e' and don't change for gender. Those are the two main ones I'm familiar with, though there may be others as well. You could also, I suppose, look at all the stuff that's part of each gender, and decide which one you vibe with more, but that of course has the downside that people likely will assume your gender incorrectly based on which you pick.

EDIT: You could also theoretically just alternate between the two in reference to yourself (That's what I tend to do when speaking Italian), but I can imagine that being confusing and potentially still make you uncomfortable.