Cross Dressing Is Forbidden (Deuteronomy 22:5).
‘ A woman shall not wear what pertains to a man, nor shall a man put on a woman's garment, for whoever does these things is an abomination to Yahweh your God.'
Cross dressing is strictly forbidden. It may well be that such behaviour was a part of certain religious rituals by which attempts were made to stir up, or even deceive the gods, but the principle was also laid down as a general one. Men should be men and women should be women, and they should be clearly distinguishable, and on principle should not wear each other's clothing. To do so would be an abomination to God. From the beginning mankind was made male and female, the former as God's representative on earth, the latter to assist him as an equal and bear children. And this distinction must be maintained and be clear to their children, and to the world.
This law respected the positions of both men and woman, and honoured their respective responsibilities. To mix them up was to dishonour both, and ignore God's purpose for each. Both had authority in their own sphere within the covenant, which must not be trespassed on.
It may also possibly have in mind what purpose someone might have in such behaviour. By this means they might spy on each other's behaviour, they might have nefarious reasons for entering into each others sanctums, they might trespass on each others right to privacy. They were blurring distinctions which were intended to be maintained, and providing themselves with a means of trespassing where they ought not to be. It made for suspicion and dishonesty in society.
“What pertains to a man.” This would include his weapons. Women were not to ape the man, or behave like men.
The modern attempt to blur the difference between the sexes is rebellion against God's way of things. In His economy each have their differing function. While male and female are all one in Christ Jesus (Galatians 3:28), stressing equality of status, this does not affect function. Each must act within their sphere. Such behaviour would also affect their children and coarsen society.