"This might feel counterintuitive" is precisely why the religious right has seized on transgender participation in athletics as a wedge issue. When they say "well, somebody who was born as a man obviously has a natural advantage over people born as women," it feels logical, right? The fact that it largely isn't supported by data rarely comes up, and when it does, it's easy to deflect with "maybe there's just not enough data yet" (which, of course, could just as easily be an argument against imposing such bans, but never mind).
It is infuriating how successful the "facts don't care about your feelings" crowd has been at pushing discriminatory legislation through in the last few years based largely on feelings rather than facts.
The classification has always been based on sociological conceptions and is still based on such after this change. There have always been outliers who are sociologically women, but don't have the biological makeup most women have.
That the criteria for admission are altered now to exclude some of them is motivated by anti-trans politics. Usually such rule changes are made when it becomes obvious that the old rules cause outcomes which go against the spirit of the sport. You cannot argue this here in good faith. There are not a lot of trans women competing and none have even won anything afaik.
I'm claiming that there were always women with outlier biology which is not at all easy to classify and not obvious at a glance.
People caring about this issue in sports now and changing the objective admission criteria to exclude them is a political phenomenon more than anything else.