I don't think the military style is the issue per se, rather than a society that is heavily gender coded, to the point that men who want to get involved with their kids find themselves constantly using female coded gear, which is a constant reminder that "you're doing a female task!" and only pushes them away / attracts ridicule.
Let them fucking have this. It's baby steps, you know?

I'm lucky France isn't in the hands of Y'allqaeda just yet, and that I ain't worried I'll catch the gay if I wear the wrong colour, but I can't imagine what it's like in the US, honestly.