Having grown up with gender dysphoria myself, and once believing that transition would be wrong, since that was the prevalent assumed view, I undertook a very long and determined search through the Scriptures to determine exactly what God had to say about what I was going through. I spent over 5 years searching, and read through the entire Bible 2 or 3 times to justify that which I, and most of you, believe. I also took it upon myself to learn and follow the main tenets of apologetics in that search. I learned a great deal, not only from the Scriptures, but from many other commentaries that I found. The ancient Jewish rabbis wrote great lengthy commentaries on the entire Law and Prophets. They did not share the interpretation already posted by several of you. Most of them viewed this verse as a condemnation of religious sexual practices that were commonplace in that day. A few interpreted this as a condemnation of a practice to include, or else exclude, one from military duty. A woman that dressed as a man in order to fight in battle was not permitted. Also, a man dressing as a woman to stay out of battle was not allowed. The interpretation that this applied to transgender individuals is a rather recent notion historically. I'd also like to point out the rest of the chapter in order to keep it in context. There are numerous prohibitions listed in this chapter. Many of them are being violated by just about everyone, including most who read this post. Including things such as the commandment to build a parapet around your roof, or to not wear clothes of mixed fabrics. The vast majority of those prohibitions are viewed as not pertaining to modern society. You cannot pick and choose which parts of a particular context are in force and which ones are not. That is solely the prerogative of the Holy Spirit. One other point to keep in mind is the context of the entire book of Deuteronomy and its purpose. God viewed the nation of Israel as essentially His wife, and the Jewish people understood this. The book of Deuteronomy was, in essence, the marriage ceremony where God and the Israelites were enjoined. This is clearly seen by reading the first chapter and the thirtieth chapter, where Moses concludes the assembly. Everything between chapter 1 and 30 was spoken to the nation at a single assembly. Take special note of Deut 30:16. This verse is basically the marriage declaration. Now, having pointed out Deuteronomy as the marriage contract between God and Israel, it is obvious that the requirements spoken within were elements of that marriage contract and do not necessarily apply to those outside the nation. That marriage was broken when the Jews rejected Christ, the bridegroom. It is because of Deuteronomy being a contract between God and the Israelites that the prohibitions apply to them alone, just as the vows spoken by any of you at your own marriage do not apply to me or anyone else, but the participants in that marriage alone.
As a side note, let me point out another interesting thing I learned about the apologetic principle of context. Context is not simply the words involved in a particular verse, chapter, or book. There is a context of time, of place, of individuals speaking or spoken to, historical, and cultural. Focusing on the context of culture leads to some interesting discoveries concerning the topic of transgenderism. Culture includes way of life, language, mode of dress, diet, and even ideological common thought. The Jews are unique in the world as probably the most effective at the preservation of their culture. Most of their attitudes and ideological perspectives remain unchanged from biblical times. Even God attested to their propensity to resist change when He referred to them as a always rebellious and stiffnecked people. With that in mind, it's interesting to find that in modern days the Jews refer to transgender individuals as "eunuchs". This is also alluded to by Christ himself in His discussions with His disciples about marriage in Matthew 19. "Jesus replied, Not everyone can accept this word, but only those to whom it has been given. For there are eunuchs who were born that way, and there are eunuchs who have been made eunuchs by othersand there are those who choose to live like eunuchs for the sake of the kingdom of heaven. The one who can accept this should accept it." I am primarily referring to those who were "born that way". I realize that many, if not most, have great difficulty accepting my decision to transition, and it does hurt me to feel the rejection of my brothers and sisters in Christ. However, I also realize in Christ's own words which I referred to that apparently most will be unable to accept it. In recognition of this fact and in light of Paul's advice to not "cause a brother to stumble" by practices that may disturb them and lead them to a judgmental spirit, I have chosen to remain celibate since regardless of who I were to choose to bond with I could foresee someone taking issue with it. Transsexuality is greatly misunderstood. Most equate it with homosexuality, which is entirely different. I believe the mistake is caused by the "sexuality" syllables within each term. This is regrettable, since transsexuality is not a sexuality issue whatsoever. Rather, it is an issue of internal nature in conflict with external nature. It's all about identity, and has nothing to do with who I'd prefer to pair with.
I find it sad how common it is for people to hold opinions which they may have thought about, but not given any research into to form that opinion. As I have indicated, I once agreed with the general belief that transition was wrong, and I spent a great deal of effort to prove that supposition. The lack of biblical evidence caused me to look deeper into it. Having done so, I then realized why God, who had been incredibly faithful to answer every other prayer and request I had ever made, was so silent with me whenever I begged Him, (for decades), to remove my dysphoria and its underlying cause from me. Effectively, I was asking Him to remove parts of my person that He had created. I was wrong.