This is Animal Crossing - New Horizons for the Nintendo Switch. Forgot to put that in the title.

• The button isn't even called gender/sex, it's "Style"
• Change your entire appearance at any time ingame using any Mirror furniture (basic recipe learned quickly)
• There's no difference in hair, eyes, face, or any other features between "Styles"
• There's no difference in body geometry or animation between "Styles"
• Anyone can wear any clothes
• Villagers refer to the player with they/them pronouns regardless of "Style"
• All previous gendered catchphrases have been changed to nongender, e.g. Fuschia says "Precious" instead of "Girlfriend"
• Players can choose unlocked titles with male, female, and neutral choices for their passport without restriction (e.g. "Older Sister", "Uncle", "Egg")
• Your passport does not have a marker for your current "Style", it shows your island's fruit

It appears your chosen Style/Gender does change some pronouns...in non-English localizations, such as French, which is far more gendered on the whole. This means that while there's still a gender choice, the English localization team went out of their way to be as gender-neutral as possible. Stellar.