> The big idea is that boys and girls, especially at high school age learn/are motivated in fundamentally different ways so splitting them and teaching them in different ways could be more effective.

This idea is even more harmful. The differences within the group are greater then the differences between the groups - but by trying to split the environments along enormously broad divisions, you're ensuring you marginalize huge swathes of people in addition to creating an unhealthy socialization environment.

The reality here is once you let in the idea that gender has something to say about people beyond what their genitals look like, you're letting in any number of other harmful ideas. It's no coincidence that girl's only highschools mysteriously lack shop-classes, for example but always have Home Ec.