In Slavic languages, which pronouns do nonbinary people use to refer to themselves? In English, its seems to have settled on "they/them" because "it" feels too impersonal, but wasn't sure if some pronouns (like ono) are preferable since there are personal antecedents (like for dijete, a neuter noun).
I'm afraid that if you need a true answer, you might need to ask non-binary persons themselves.
Anyway, from my perspective, using a non-binary pronoun to describe
oneself would sound awkward and unnatural, to say the least.
That's because unlike English, in Polish - and most, if not all, Slavic languages - verbs (at least in some tenses) and adjectives (always) are inflected to agree with the gender of the subject of the phrase. And in Polish, as well as in other languages I have a grasp of, only masculine and feminine gender verb forms exist for the first and second person singular, and the use of the second person singular neuter gender is pretty marginal. Leveraging the patterns for other persons and genders you can inflect the verbs to a neuter form of the first person singular*), but it would be a neologism.
To give you an example, let's take "to read" in the past tense:
1. ja czytał
em (m), ja czytał
am (f), - (n)
2. ty czytał
eś (m), ty czytał
aś (f), ty czytał
oś(n)**) - extremaly rare, probably used only with "dziecko" (child), which is neuter gender noun)
3. on czytał (m), ona czytał
a (f), ono czytał
o (n)
While in English you have the same form ('read') across all the persons, so you may use any existing or invented pronoun you like.
As for the first person singular, typically the humans have identified themselves in a binary way, and usually one knows their own sex or gender (whatever they prefer to use). And the language reflects that. Even in the fairy tales a talking animal would use grammatical forms matching their true sex in the story (if it's known) or a grammatical gender of the animal name. Same for talking plants and inanimate objects.
With the adjectives it's somewhat easier, as they have all three gender forms, and don't have persons.
*) Actually, I've found a neuter gender first person form used once, for artistic purpose in a sci-fi short story by Stanislaw Lem. It was written from a perspective of an AI in a robotic body and it used first person neuter to describe its initial, blank state of mind. When it it confronted a group of humans and realized that it had a body of a woman it switched to regular feminine gender pronouns and verb forms. I wouldn't be surprised if it was the only use of this form in the history of Polish literature.
**) Normally you address someone using binary gendered forms of the verbs. If you address a child, it's possible to use 'dziecko' (child) as a sort of a pronoun (usually for emphatic reason), and, consequently, second person neuter verb form, to agree grammatically with the address. Like 'what have you done, child?!, Dziecko, coś ty zrobił
o?!'. The only scenario, I could think of.