It's not grouping them as boys and girls that is outdated and absurd, it's the idea that that is how it's supposed to be done that is stupid. Even if the OP article wasn't about gender identity, what's wrong with mixing things up? Why not mix the kids up and make it clear they are equals and alike in many ways, rather than keeping them as two separate groups that are only defined by the same two categories over and over? Actually, why not have them form into three or four groups to show life is hardly ever a clear cut black-and-white, either-or process?
I'm gonna put up my hand right now and say I have not read the majority of posts here, just a quick skim (15 - 20 posts, tops). So if I make less sense than usual, feel free to disregard.
When I was teaching, we'd rarely split kids into gender based groups over the course of a 'normal' school day.
Commonly, we'd split them based on proficiency in whatever we were teaching at the time.
So, no, there wasn't a 'turtle' group of slow kids, and an 'eagles' group of stars. If I was teaching division, each kid would get personalized problems on the topic at hand, and I'd work with a group of kids of a similar level on a particular aspect. Might be the kids who needed extension, might be those who needed support, might be the middle ones, since there was the risk of them not being attended to as much.
Groups were fluid based on proficiency.
When going on school camp, different story. Dorm rooms were gender divided, for much the same reason toilets were gender divided.
So from a practical point of view, groups were commonly gender divided as well.
I had a bad habit of referring to the kids as 'guys'. I actually connected really well with the girls, since they were a little more mature than the boys overall. But yeah...guys...
Children is okay, but way too formal for my teaching style. And I wouldn't go with an arbitrary name imposed by the school. Again, just not my style.
So, if the school wanted to have gender neutral names for children, I'd go with kids. Or I'd let the kids pick something they wanted to be referred to as, which would probably end up being 'Superstars' or something. Or I'd just call 'em my horrible beasts.
Tangental side story:
I had a deal with one of the Prep grades when I was teaching Grade 3's. We wandered into their class at a preset time, but my class was convinced we were invading them. We planned it all out. In we marched, no-one saying a word, then formed a conga line and danced around their class. One lap, then out.
The funniest part was when payback came. Not only did the prep's come and conga-line-bomb our classroom a couple of days later, but they did so dressed up in monster masks they'd made themselves in art.
Wish I'd taped it, it was hilarious.
Anyway, approximate point to this is that kids like belonging to groups, and for practical reasons we need to divide kids into groups. But very rarely does this need to include gender as a determinant.