The obvious solution is introducing a gender verification system next to the age verification system (obviously also has to be implemented by a private for-profit company with minimal oversight because anything else would be socialist and evil).

Then, kids could either upload their government id or a picture of themselves naked. Those pictures have to be kept around indefinitely because security and analytics and feeding them into an ai model.

Then (because genitals always 100% identity someone's real sex and everybody has a real binary sex) the kid can only select the appropriate character! Simple as that!

(This is probably the worst thing I have ever written. But it doesn't feel implausible that someone would actually suggest this, which I think is testament to how bad the situation is.)