Ever heard of The Ginsburg Rule? Since RBG's confirmation hearings in the 90s it has been normal and routine for every Supreme Court nominee to decline to provide an opinion on matters that may come up before the Supreme Court. Expressing an opinion beforehand without knowing all the facts of a potential case could be seen as evidence of bias, so nominees avoid doing it.

Kavanaugh and Barrett did the same thing in their confirmation hearings when topics like abortion came up. If seems likely that a transgender sports case could rise to the SC in the near future, just like abortion related cases are hitting the SC right now, so expressing an opinion on the definition of a woman is reasonable to avoid, since that could be one of the central issues in a future case.

Also it was just grandstanding bullshit by the republicans and wasn't a serious question worthy of engaging, but that's a whole different issue with the way all confirmation hearings are handled these days.