I want to address individually objections that trans people face by using Christianity or Christian-like reasoning and give some good, old fashion apologetic answers.
Genesis 1.27 God created humanity in God's own image, in the image of God, God created him; male and female God created them.
Exodus 20:17 Thou shall not covet. To transexuals covet their gender of others?
Deuteronomy 22:5 A woman shall not wear man's clothing, nor shall a man put on a woman's clothing. Whether this verse is relevant to trans people.
Deuteronomy 23.1 Whether a verse about crushed genitals disqualifies SRS.
Matthew 19:4 Have you not read that who created them from the beginning made them male and female?
1 Corinthians 11.14-15 If a man has long hair it is a dishonor to him.
Christ and the Bride Using the symbol of Christ marrying the Church to dictate earthly marriage.
The Alternative Repression - Therapy (or prayer, marriage, etc) can change your feelings feelings
Trans People Cannot have ChildrenOften these arguments all have the faulty assumption from the Sex/Gender Binary that people are either male or female. Intersex people prove this wrong. In the article Effect on Binary Arguments, I show quickly these arguments fall apart when taking intersexuality into consideration.
Transgenderism is a Slippery Slope
Transexuality Is Gnostic
God Does not Make Mistakes
Another group of objections to transgenderism revolves around mere semantics. These arguments come in two flavors. The first (including Sex Cannot Change, Gender Cannot Change, and Transexuality is Homosexuality) misunderstand the meaning of a word and then show how their false meaning is incompatible with transgenderism. These errors can always be resolved through simple education such as reading my Trans 101 or simply having a close relationship with a transperson and listening to them explain themself.
The second flavor (including Deception and Mutilation) is your everyday smear tactic. A word which has a negative connotation is applied to a transgender act and all the negativity of the word is applied to the practice. These do not even attempt to be logical arguments; they are rhetorical devices and efficient ones at that. Consider such a tactic taken against Christians. The early Church refused to pledge allegiance to their nation because, unlike many modern Christians, they believed they could not "serve two masters" and chose following Christ to the exclusion of the Roman Empire, Israel, and others. Christians were branded as unpatriotic and this was entirely accurate. Then, as now, being unpatriotic was considered a moral vice and thus the morality of Christianity was attacked. The weakness to this argument is that patriotism, while it sounds virtuous, is not always so.
See also Semantics.