I have not seen evidence that keeping these topics sensitive is a good thing, so I think the burden of proof is on you to justify why they should be "kept sensitive". Notably, the "shame" around periods routinely gets challenged by concerned parties. Additionally, "keep sensitive" is a weird euphemism for the original, much stronger claim that boys can't truly be boys unless there are no girls.

I have a buddy who's been a scout from youth til college, and the net impact of gender-segregated scouting in the USA vs. most other countries in the world is that american kids were clueless and out of place at the global jamboree he went to, since other countries have correctly obsoleted the stupid divide.

If puberty is a salient point for you, maybe you need to group slightly older boys with slightly younger girls. However, before that, you'd need to justify why these developmental differences matter at all for the vast majority of socializing kids do.

And ultimately that's my problem with your post. You are very scared about the idea that some of these cultural gender barriers may be torn down, and you have some biological facts in hand, but you haven't actually made a case for why these biological facts necessitate the erection of cultural barriers. The burden of proof is on you, despite the american status quo lagging behind.