The humane and logical solution presents itself to anyone of good faith trying to solve this:

Everyone gets to compete. Not everyone gets to compete against girls.

1) (XX-chromosome) women's division and

2) Open division for anyone with XY chromosomes and anyone else that wants to compete with them, no questions asked. This preserves privacy, dignity, and competition. No need to measure testosterone or get private parts examined. Also, it reveals if people actually want to compete or if they are just here to beat up on girls having somehow discovered a nominally progressive way to do so.

This opens the prospects for some women such as Mikaela Shiffrin or Courtney Dauwalter winning both. Bring it. The boys better ski/run faster if they want to stay ahead.