One of the scriptures that is used against transsexuals is found in DEUTERONOMY22:5 where it states: "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." But they completely ignore one's gender identity and say that you are the gender you are by your chromosomes which can't be changed. But they refuse to acknowledge where there is more than one indicator that can determine gender identity which could be different than one's biological gender which makes one trans.
Now this passage could be used against those fundamentalists. Ecclesiastes 11:5: "As thou knowest not what is the way of the spirit, nor how the bones do grow in the womb of her that is with child: even so thou knowest not the works of God who maketh all."
This passage notes that humans cannot know how a fetus is formed in the body of a woman. This is a work of God and cannot be fully understood. This might be interpreted as implying that we must accept, value, and support God's handiwork, including newborns formed with a brain gender opposite of their genetic gender. Another one we can use for them as well is this one.
John 7:24: "Judge not according to the appearance, but judge righteous judgment."
This is a command from Jesus that we stop judging people according to their mere appearances and go deeper. This might be interpreted as accepting a transsexual's perceived gender identity instead of concentrating solely on their genetic gender.
But they could counter with this one though.
1 Corinthians 6:18-20: "... know ye not that your body is the temple of the Holy Ghost which is in you, which ye have of God, and ye are not your own? For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God's.
Some who oppose gender transitioning interpret this passage as requiring a person to accept both their body (including their genetic gender) and spirit (including their gender identity) as creations of God. Thus a transgender individual should accept their conflicts over gender without resorting to hormone treatments and/or gender reassignment surgery.