The people angrily shrieking about trans girls and trans women participating in competitive sports absolutely do not care at all about girls' and women's sports. They don't care about equality or fairness or opportunity for female athletes.
At all.
They talk about how unfair it is if a trans female athlete gets a scholarship and takes it from other girls. They pretend like it's super unfair. But if you just take that scholarship away from the girls altogether and give another one to the boys, they'll be happy about it. They will rejoice, and if you complain about it, they will erupt in spittle-flecked anger over how unfair it is to give the same number of scholarships to male and female athletes.
These people and their shitty parents and their shitty grandparents have been bitching and moaning about how unfair Title IX is to boys, how unfair it is to give equal money and opportunity to male and female athletes, for as long as Title IX has existed. They don't care about women's sports. Every one of them is gleefully spiking the ball and celebrating over Brittney Griner's incarceration as a political prisoner in Russia. They love it.
But they hate trans people even more than they hate gender equity in sports, so they will gladly dishonestly make gender equity arguments in order to attack and express their contempt and disgust for trans people. Especially trans kids — the trans people that they despise most of all.
They're not inconsistent or hypocritical. They don't care about the inconsistency and they don't care about the principles.
They're just bigoted fucking liars.