I think they could run into issues with an open category and it might be where men start making noise about their rights.
Much of it could be around language used - if your category is 'Open' and you, a man, win a race or set a record is it called a men's record or an open record? Men may well want to be able to name their records and medals as men's.
So let's say the category is called Open but men who win are still allowed to call their wins mens or males what happens if a male person who has a female or NB identity wins (possible if that person has had no hormone treatment)?
What is that person's win recorded as? Can't call it a female/women's record because that still impacts the protected female category. So we are back to calling and recording everything as an 'open' record and an 'open' medal.
Thing is I don't think for a second any sporting bodies and not many male athletes are going to stand for men's sport being erased in name. If fact it's probably one of the reasons why all this stuff has been shoved onto women in the first place to avoid it impacting men's sport in any way.