How do we make that work? I want transgender kids to be treated equally, and I want girls sport to thrive. How to achieve both?

I don't know. Unlike most questions relating to trans rights, competitive sports for older kids and adults present some challenging issues that, although they arise in a very very very small number of situations, don't admit easy solutions. That's because the reason we segregate men's and women's sports today has nothing to do with the sociological construct of gender, but the biological aspects of sex characteristic.

One possible answer, of course, is to observe that there really isn't any practical inconsistency between the two goals right now. Given the trivially small rate of participation in sports by trans girls, their participation can't keep girls sport (writ large) from thriving. A very small number of individuals might end up having advantages because of their genetics and biology - but not often enough to have much of an impact. Plus, that happens in other contexts, and it doesn't keep those sports leagues from thriving. To use a trivial example, if you're competing in USTA youth leagues in the younger brackets and you haven't completed puberty yet, you're going to get crushed by the kids who have - no matter how hard you work, no matter how hard you practice, an 12-year-old who hasn't hit puberty will get demolished by someone who has completed puberty, OTBE.