Doubtful even with a conservative court...at least not without unintended consequences that spill all over the place (such as a serious gutting of Title IX's male/female balance). If you have an "open" division it directly undermines the proposition that female sports have to be treated equally....they are no longer equal...they are a subcategory akin to a disabled category of the larger "open" division". Unintended consequences. If you don't, then you are on the same footing as disabilities: if you extend accommodations for disabilities, it's hard to see how you don't for the trans, even if it's just under a proposition of separate but equal. Hard to predict, but in the US, barring the acceptance of some sort of rational compromise, or the Rs taking both houses of Congress overcoming the fillibuster and getting the Presidency, I think it comes down to a blue state/red state split. Long term, I think Europe leads the way and where they come out on things.
In any case, Title IX and women's athletics may be about to be turned on their head in the event women's football catches on in the next 3-5 years. If it does (I'm not convinced it will but I saw a demonstration in Sherman Oaks Park a few months and the players really seemed into it), soccer and volleyball in particularly are going to be greatly impacted. If I had a DD that was 5 or 6 right now and looking to direct her to a sport, I'd be looking at this carefully to see how it develops because if it takes off (a big if) it's going to turn everything over on its head.