Here's how crap like this works.
Once upon a time, no one thought that very many people would wish to change their gender, let alone compete in sports while doing so. Those people wrote up some rules for high school competition that were intentionally very vague to guarantee that women and people of color could compete in sports. At the time, this pissed off a bunch of extremist people, but common sense and fairness prevailed. High school sports flourished and lots of people that had been shut out of sports for various reasons.
Jump forward a few decades and a handful of transgender individuals want to utilize those same vaguely worded rules and bylaws to have their chance to compete in scholastic sports as the gender which they identify as. No one worried about it until some male-to-female athletes not undergoing hormonal treatments or gender affirming surgery started winning titles. International bodies were quickest to act and implemented rules to keep their respective sports fair. Those changes have no effect in American high school sports and absolutely no standing in U.S. courts. That is why we find ourselves in the current situation - legally, no one is able to stop MTF athletes from competing as women in high school.
OK, let's change the rules! We'll make it fair for all and create a path for transgender athletes to have equal opportunity to participate. "Not so fast!", say the lawyers, "You must allow my client to compete as a fully recognized woman or else we will sue for the right to compete as women AND we will seek damages!".
In these tough times, no school district or state athletic authority can afford to mount multiple legal defenses nor can they chance losing. If you live in a red state, your legislature is probably going to pass some poorly written and emotionally charged law into place that will likely not pass Constitutional muster and court challenges. Those legal cases will take 5-8 years to end up at SCOTUS only to be tossed out.
Live in a blue state? Your legislature won't do anything about it for fear of looking bad or because...why? It's not their core voters upset over this. They will just circle the wagons and, in time, some other cause like police reform, affordable housing, or universal preschool will crowd out this non-problem.
This really isn't a problem that can be laid at the feet of any political party. Just as Madison couldn't envision machine guns, bump stocks, and hold ups when he drafted the Second Amendment, pre-2000s Republicans couldn't foresee transgender school sports being an issue. The Democrats? They didn't cause this either. There is no legislation that guaranteed access to high school sports for transgender people, just measures that protected such people from discrimination in hiring and housing. Sure, they want to talk about it now and hit each other with it but see my points above as to how they cannot effectively deal with it.
I don't know what the solution is. What I do know if that no one seems brave enough to craft a pragmatic solution or to find a fair middle ground. Sadly, this is going to be with us for a while because I don't see things changing. Both sides can get TV time and fundraise off of it so letting it fester serves a purpose. For those of you with daughters in the crossfire, make sure that you support them, advocate for them, and let them know that their athletic journey means far more than a medal at state. Talent still gets recruited and collegiate coaches live in reality.