Mostly for myself, I'd like to use this blog post to outline what I do and don't know about transgender issues.
First, it bothers me that part of the definition of gender identity disorder is that a person prefers stereotypical activities, friendships, and clothes of their "true gender" rather than their physical sex. As a man who usually prefers female friends, who loves cooking and reading and writing, who relates better to women in most ways, and also as a psychology grad who is highly skeptical of stereotypes, I think we need something better to go on.
Second, contrary to common LDS opinion to the contrary, I can find no canon, doctrine, or consistent Apostolic teaching that it is impossible for a male spirit to be born to a female body, or a female spirit to be born into a male body. I see no doctrinal explanation for hermaphrodites. On this matter, I can only say, "[I] believe that God will yet reveal many great and important things pertaining to the kingdom of God" (Article of Faith #9).
Third, Latter-day Saints have a unanimous Apostolic statement that gender is eternal, applying to spirit and body alike. Therefore, the gender of the spirit is of paramount importance.
Fourth, I don't know what it is like to believe that your true gender and physical sex are at odds. I don't know what sort of support, therapy, or counseling such people would need. But I know that the Savior knows, because if he experienced every sorrow, temptation, and imperfection of humanity on the cross, then he experienced the sensation of gender identity disorder.
Fifth, even if spirits can be born into opposite-gender bodies, it seems likely to me that there are people who believe that they have a spirit-body gender clash, but who really just don't relate to gender stereotypes. People like me: I have a male body, a male spirit, and strong feminine tendencies. If I am right, and there are people like this, then a sex change operation is not what they need. They need to see how foolish stereotypes are, and to embrace being a "feminine" man or a "masculine" woman: we have women of strength, determination, intelligence, and boldness, and we need them; we have men who are gentle, nurturing, relationship-oriented, and wise, and we need them.
Sixth, the Lord has to be the ultimate judge. He knows the gender of each spirit, the needs of every soul. He alone can care for us as we truly need to be cared for.