Cross dressing simply put, is wearing the apparels and garments that belongs to the opposite sex/gender.
Cross dressing in most ‘advanced’ nations of the world has become a norm in the society, but what does God and the bible say about this act, is it right or wrong for Christians to cross dress?
The bible in Deuteronomy 22:5 gives a clear understanding of the topic of cross dressing and transvestism [women dressing in men attires and vise versa].
From this passage, God instructs and command that a woman should not put on that which pertains to a man, and a man is not to put on that which pertains to a woman as well, because anyone who does this is an abomination unto God.
The message in this passage is not intended to forbid women from wearing pants of trousers, or to forbid men from wearing skirts/kilts [the Scottish traditional men].
It is solely focused on the fact that anyone who cross dresses, is trying to appear as something or someone else, that he or she isn’t, and this could be used as a means of deception.
The true definition of cross dressing from this passage, is changing one’s apparel and appearance to look like the opposite sex, and this is not acceptable to God because it discards the natural use of things, and takes on that which to God is unnatural [ Romans 1:24-27].
Apostle Paul in his first letter to the Corinthians in 1 Corinthians 11:3-15 tells the Corinthian church that the way and manner in which a woman adorns herself, and wears her hair is a reflection of God, likewise also a man.
Therefore, any woman who cuts or shaves her hair just because she wants to appear like a man, and a man who grows out his hair just because he wants to be seen like a woman is bringing shame to the body of Christ.
This doesn’t mean that any woman who shaves or cuts her hair, or any man who grows out his hair is a sinner, it is acceptable to keep one’s hair in whatever form or style that is most suitable to one.
It only becomes a sin when the motive and attitude of one’s heart for doing such thing is to appear as someone else, and like we know, that is deception, and deception in itself is a sin.
Christians should take note that different customs and traditions calls for different gender related clothing, for example it is customary that a traditional Scottish man wears a kilt[skirt].
Therefore, in such situations a man wearing a skirt is not crossdressing.No matter the custom and tradition of any society, Christians should only wear what is gender appropriate in that custom and make sure to dress decently, and above all bring glory to God.
https://www.gotquestions.org/cross-dressing-transvestism.html