Women’s feet are different but also the shape of a woman’s shoe is different from a man’s. Men’s shoes tend to emphasize the length of the foot and women’s tend to try to make your feet look smaller. Photos of shoes for sale online are often just photos of the shoe without anyone wearing them and you can still tell which are women’s shoes.
Wearing men’s shoes looks like you’re wearing men’s shoes. It’s very much like wearing a smaller size of a men’s shirt. It’s not that you can’t put it on but it sure doesn’t look like a shirt tailored for a woman.
I’m not sure why a military outfitter would sell brogues or really any dress shoe.