Deuteronomy Chapter 22
Deuteronomy 22:5 (King James Version) The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman's garment: for all that do so [are] abomination unto the LORD thy God.
Respected conservative protestant, Jewish and Catholic commentators provide background information that makes the position that this text is about idol worship seem credible. The Jamieson, Fausset and Brown Commentary indicates disguises were worn at times in "heathen temples." The respected commentator Matthew Henry states that some people feel this text is in reference to a custom in idol worship. Men who worshipped Venus might dress in women's clothes and women who worshipped Venus might dress in armour. One position about the text that the Jewish commentator Jeffrey Tigay presents is that this text is about "pagan rites and majical practices." The Catholic New Jerome Biblical Commentary also points to the possibility this text forbids cultic prostitution.
Given the strong possibility this text is not about wearing the clothing of the opposite gender but is about idol worship, this text should not be used to condemn or criticize transgendered people. We owe it to transgendered Christians and to God not to condemn or criticize people when the there is doubt the Bible opposes those transgendered people who cross-dress.
Transgendered, cross-dressing Christians are not acting as prostitutes in pagan temples. Cross-dressing in modern society is not an act of worship to another god. While worshipping another god is strongly condemned in the Bible, there is scant Biblical evidence that cross-dressing is a sin.