I'm an atheist, but I was sent to a school for fundamentalist Christians. I would say something along the lines of this.
Someone who is transgender is not a mistake. ->-bleeped-<- exists because there is sin in the world. Since the fall of man the human race has faced birth defects and disorders(Romans 5:12). I am not transgender because my parents or I have sinned. Like the blind man in John 9:2-3, His disciples asked him, "Rabbi, who sinned, this man or his parents, that he was born blind?" 3 "Neither this man nor his parents sinned," said Jesus, "but this happened so that the works of God might be displayed in him. It is hard to understand, but God's ways are higher than ours (Isaiah 55:9). The Bible does not say anything directly about being transgender, but it does acknowledge that there are those who fall outside of gender norms. There was not even a word for transgender back then, but Matthew 19:12 reads "For there are eunuchs who were born that way, and there are eunuchs who have been made eunuchs by others—and 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." In many ways I am like a eunuch and I have learned to accept myself.
I need to find comfort. Transitioning makes this possible. Without transitioning I will not be able to live on and serve the Lord. You may not agree with this, but it is my burden to carry. You may think I am sinning, but even if it is, that doesn't make me less of a Christian. "Indeed, there is no one on earth who is righteous, no one who does what is right and never sins (Ecclesiastes 7:20)." Just like the woman in John 8:1-11, I expect those who view my actions as sins to judge me harshly. I also expect others to talk poorly of me even though James 4:11-12 says "Brothers and sisters, do not slander one another. Anyone who speaks against a brother or sister or judges them speaks against the law and judges it. When you judge the law, you are not keeping it, but sitting in judgment on it. 12 There is only one Lawgiver and Judge, the one who is able to save and destroy. But you—who are you to judge your neighbor?"
I hope that we can remain friends though this. Galatians 6:2-5 says to "Carry each other's burdens, and in this way you will fulfill the law of Christ. 3 If anyone thinks they are something when they are not, they deceive themselves. 4 Each one should test their own actions. Then they can take pride in themselves alone, without comparing themselves to someone else, 5 for each one should carry their own load". " There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus (Galatians 3:28)."
Here are link to the verses I didn't write out or explain.
John 8:1-11
http://www.biblegateway.com/passage/?search=John%208:1-11&version=NIVRomans 5:12
http://www.biblegateway.com/passage/?search=(Romans%205:12&version=NIVI used the NIV version for all the scripture.