There are some areas where this is possible. Razors for example: In my experience woman’s razors are absolutely shitty and more expensive then men’s razors.

But concerning other areas: There might be a chance, that a significant number of woman doesn’t want to smell like „Old Spice“ or „Irish Moss“ and most men’s clothing does not match with most women’s body’s. Also I think you underestimate how it could completely wreck a kids social life, if wears the „wrong“ clothing or plays with the „wrong“ toys.