Apparently it's nothing to do with changing the gender, only opening the character creation screen. So you can open that screen and then just close it, and it should work again. Weird bug though!
If starfield works like every other Bethesda game, the game can't actually change the gender directly, it instead remakes your entire character, which will reset whatever is causing the bug
I had a bug caused by the shipselling bug where each time I went through a load screen my gender and appearance randomized. So I can't even begin to guess how all the noodles are connected.
The article links to a story about some YouTubers who went on a rant about the optional pronoun feature, so yeah, I could absolutely see this getting blown out of proportion.