Question: "What does the Bible say about cross-dressing / transvestism?"
Answer: Deuteronomy 22:5 deals with the issue cross-dressing / transvestism (men dressing in women’s clothing and vice versa). In this passage God commands that a woman is not to wear that which pertains to a man and a man is not to wear that which pertains to a woman, for all that do so are an “abomination.” The Hebrew word translated “abomination” means "a disgusting thing, abominable, in the ritual sense (of unclean food, idols, mixed marriages), in the ethical sense of wickedness." Therefore, this is not simply God addressing the fact that a woman might put on a man’s garment or vice versa. Also, this is not a command that a woman should not wear pants/slacks as some use this passage to teach. The meaning here is that this “cross-dressing” and transvestism is done in order to deceive, or to present oneself as something that he/she is not. In other words, this speaks to a woman changing her dress and appearance so as to appear to be a man and a man changing his dress and appearance so as to appear to be a woman. This is the definition of cross-dressing or a transvestism.
We can also reason that the dynamic behind this is the leaving of what is natural and taking on that which is in God’s Word called unnatural (Romans 1:24-27). Paul tells the Corinthian church that the way a woman wears her hair is a reflection of God’s order, and therefore a woman who cuts her hair to appear as a man or a man who wears his hair long to appear as a woman brings shame to them (1 Corinthians 11:3-15). The issue here is the motive and attitude of the heart that is evidenced in the choice to rebel against God’s standard for obedience.
These are principles we can use to reason an application. Whatever the prevailing custom, men and women should wear gender-appropriate clothing, dressing decently and in order (1 Corinthians 14:40). To apply the principles, the Bible calls cross-dressing or transvestitism a choice that is a demonstration of unbelief and rebellion against God and His order.