My supportgroup does schooltraining and for a work for school I investigated on gender-aware schools and teaching, which despite the very effective distracting and sensationalising the author uses is what this is about
. First things first is that it's not 'for' gendervariant children, it's for every kid. Splitting classes up by gender is one part of it, and is simply not needed. The reason why they'd prefer not to do that is because it encourages the stereotypical thinking about boys and girls (not beneficial for anyone, including perfectly binary non transgender kids) and because you're then constantly encouraging boys to only mingle with boys and girls with girls. But it goes further then this and is most important in the younger years, start early! It's also about not making every girl-thing pink, about using books that don't always talk about the lady who is a stay at home mom and de man who works in building... About not avoiding stereotypes but being aware of it. About being inclusive of all diversity, of girls that like technical stuff and boys that like sewing.
From the very beginning kids are being pumped full of ideas about girl/boy and not suprisingly this effects them greatly in life choices, behavior, clothes... Gender-aware teaching isn't about changing the school for those few kids that are gendervariant. It's about changing schools to a system that is beneficial for every single kid!
Another last point is that it isn't about avoiding boy/girl either, not pretending there's no such thing but being aware that a lot of the splitting we do is simply not realisitic and that we as adults are confining our children in our own little boxes when it's simply not necessary. In Belgium this is being promoted for kindergarden but I'm not sure US has that? 3-6 years old? This is pretty much THE age to start teaching kids stereotypes are just that, stereotypes. It also goes into further diversity like skin colour, different views, different looks... It just allows kids to grow up less confined by their gender and more about who they are and what they're good at. Gender is only part of that but in our current society everyhting is seperated by this, it's even on our ID's.
I can't really make up my mind about the policy, because well, someone who really wants to make it very negative and ridicule it has written the article but some of the things he ridicules are defintely good things in my book. Also I'd totally want to be a purple pinguin! :p (sorry for my english, I'm belgian)