I think the idea of "cross dressing" reinforces gender stereotypes. Clothes are just clothes, and the expectation that some clothes are only for men or only for women is only a mere step or two from the idea that there are certain clothes that women and men should wear by dint of being their sex.
I feel like we took two steps away from this idea around the 60s-80s, when every other male popstar was wearing makeup and women were rocking dungarees, and have since taken a step back toward the idea that there's something "wrong" with people who have a preference for more masculine or feminine ways of dressing.
High heels for men were fairly common in the early 17th century, as were brightly colored clothes, wigs, tight-fitting breeches (leggings), makeup and other adornments. For a multitude of reasons, including enlightenment ideals and the need in France for people to disassociate themselves from the royals for fear of being attacked by Jacobins during the revolution, men's clothing became far more muted and boring in the 18th century. Included in the transformation of male fashion was the strong undertone that men were practical and utilitarian while women, who kept their colours, adornments, wigs and makeup, were frivolous and emotional. Look up "The Great Male Renunciation" (GMR).
There was even a movement - the Men's Dress Reform Party formed after WWI. One of its founders, John Flugel, a psychologist, opined that the GMR was when men "abandoned their claim to be considered beautiful" and "henceforth aimed at being only useful".
I think men who are interested in fashion, who want to wear heels and makeup and sparkly spangly adornments and bright coloured skirts should be absolutely free to do so without any negative assumptions being made about them. Just like I'm free to wear a navy pants suit to be a bridesmaid (true story) and forego all those things because they just don't interest me.
Maybe if they were, there'd be less children and teenagers thinking they must be the opposite gender because they like (or don't like) the pink sparkles.