In his note for this verse in “The Pentateuch and Haftorahs”, editor Rabbi JH Hertz writes that, “An interchange of attire between man and woman would promote immodesty and, in consequence, immorality. This law is probably directed against rites in Syrian heathenism, which included exchange of garments by the sexes and led to gross impurities.”
He speaks here of transgenderism, which is serious sin.
Personally, I have very little problem identifying women from men. Of course, I’ve been married for 42 years and therein lies some difference.
The IDF has suffered because of women in combat and it will continue to suffer. It’s compounded folly.