Thou Shall Not . . .
The quick answer regarding changing one's sex is "no" (with the possible exception of those born as hermaphrodites). This conclusionhowever has to be indirectly derived from Scripture. To be honestthere is no text that says"Thou shalt not alter thy sex."
The Bible does make clearhoweverthat God did not approve of men making themselves eunuchs (which kind of made them gender neutral). Such an actwhether carried out willingly or performed against a person's willstrips males of the ability to sire children by removing their sexual organs (Deuteronomy 23:1).
Eunuchseven though they lost the ability to procreatecould still serve the Lord (Isaiah 56:3 - 6Acts 8:27 - 39). Many of themsince they were slaveshad little or no choice about their sterilization in such a gruesome manner. Deuteronomy 23 seems to indicate that people should not voluntarily choose to mutilate their reproductive organs.
A fundamental limitation of modern procedures for changing genders is that the organs implanted or created are not fully functional. A man who tries to become a woman will not be able to give birthnor will a woman who becomes a man be able to sire children through intercourse. They are merely trophies or symbolsnot a functional reality.
Thereforesomeone who feels he is a woman trapped in a man's bodyor vice versaneeds to visit someone specialized in psychological counseling before he or she would surgically mutilate himself or herself in order to "change" their gender.
A Surface Change
It should also be noted that gender is not just a matter of the reproductive organs. Its imprint is on every cell through the XX or XY chromosomeincluding in the brain. As a resultalthough someone can take hormonal drugs and undergo surgeryhe or she cannot really change his or her gender at a fundamental level.
The mindset imprinted in a developing fetus' brain by the presence of testosteronefor exampleis not removable decades later long after birth by taking estrogen.
It is much better for people to learn to accept who and what they are physically rather than trying to change their gender surgicallysince the results are so crudely limited compared to what would theoretically have to be removedalteredor both in order to transform someone's gender.
Biological Differences
The differences we see between men and women are not mainly created by society but reflect biologically driven (which was created by God) realities. By accepting the teaching of Scripturewe merely accept what we could discover and reason from nature based upon anthropological and sociological studies.
Conclusion
The Bible generally does not approve of a gender change. Although we cannot cite a direct text on the matterwe can make a conclusion based on the evidence available.