are these laws specifically to keep kids from having fun playing sports with zero stakes?
these are laws specifically to oppress trans people and put a wedge between them and "the rest" by fearmongering and othering, from as early as they can possibly manage.
Even with big stakes, trans women in sports is not a "problem" it never has been, if it was they would be winning a lot more medals, I'll tell you that. But they aren't, because they don't have any advantages over cis women just by virtue of being trans (if anything, they have significant disadvantages like being the target of so much hate).
This is 100% motivated by bigotry under the guise of "think of the children!!1"