The first warning comes from Deuteronomy. It states a man should not wear that pertaining to a woman nor should a woman wear that of a man. The reasoning behind this is that it will cause confusion. This is more akin to the "Transvestite" community. Transsexuals take that one step further by not only dressing as the opposite, but also being physically altered to appear as the opposite sex.
I'm writing this from memory, but as I recall, in Isaiah, God says "i formed you in your mother's womb". Here, God is saying that He created a person a certain way. It's in their DNA the way God created them.
Then in Romans 1, we read that people reject the truth of God for a lie and they burn in their own lusts. People change their very selves. In a strict interpretation, it talks about women with woman and men with men. This is the most straight forward verse in the whole Bible about homosexuality. But the key here is that people are forsaking the truth of God for a lie. They do this in pursuit of their own lustful desires. As Jesus said, "God created them both male and female so a man will leave his parents and cleave to his wife."
Why is this important?
A person is rejecting that God made them (either male or female) by transitioning. They are then uniting with someone in a relationship that does not reflect God's original design of one man with one woman.
Looking at 1 Corinthians (6, I believe), Paul writes to the church at Corinth that "such WERE some of you". This in context is with a list of people living sinful lifestyles. Pornea is used in this passage which is a general term for all sexuality outside the 1 man married to 1 woman dynamic that God originally sent. The key to this verse is that the WERE statement means that transsexuals (like everyone else) have the ability to change. Choosing to change is their first step toward serving God.
Above all, the Bible starts (Genesis 2) with God saying "Let us make man in OUR IMAGE". From this we're seeing that all are made in the likeness of God. People may pervert this through sin, but all are still made in HIS IMAGE. Thus, all are deserving of respect.