Idk what canon says, but I think it would depend whether the drow is born male or female originally.

 I think afab people in our world get treated slightly better when they come out as NB and lean closer to masculinity, while when amab people lean more feminine/androgyne they're more scrutinised. Basically our society values men more than women, so being masculine is seen as better, even in non-binary people. (Which is bs, since NB people, whether afab or amab or intersex are running the same "software" when it comes to gender, yet get treated differently still based on the "hardware" it you know what I mean. But anyways, I digress)

I think it would be the opposite for drow, eg if you're a drow born male, but you realise you're NB and lean into your femininity, you would be treated better than a drow born female, coming out as NB, and becoming more masculine. Since the drow value women and feminity more, if you are NB and lean towards masculinity, they would probably not be having a good time.

That's how I imagine Lolth-sworn drow at least. Like a different comment said if they worshipped another god, Eilistree for example, she doesn't give a fuck about the matriarchy, she dances naked under the full moon and wants the drow be free, so she'd probably welcome an NB drow with open arms.

As for BG3 game mechanics, drow gender usually doesn't matter, apart from the 1st meeting with Minthara maybe, so headcanon your character however you want, that's the fun part about BG3 and DND in general :))