[Yes, it's 26 minutes long... and yes, I do recommend this as the summary alternative to 500+ pages of reading.]
Disclaimer: The video includes a lot of cartoon illustrations of reproductive organs and one small-scale, black-and-white photo of a naked CAIS subject in a stance that resembles a police lineup photo. I don't recommend watching it at work, and would suggest giving your spouse a heads up on what you're about to watch before hitting the 'play' button so they don't come to any incorrect assumptions on first glance over your shoulder. That being said, it's not pornographic in any way (unless you're a subscriber to Comstock's definition, in which case you're welcome to enjoy a life of deliberate ignorance) and is something I would show my children (if I had any).
So yeah... watch the video, and then read the rest of this blog post.
Now that we've established the MEDICAL nature of gender identity and all things sexual (You did watch the video, right? No cheating; do it!), lets get back to the "So what?" question.
Trans people don't choose to be trans. It's a biological phenomena that, for reasons that we may never be able to precisely identify, manifests prior to birth. Note that birth is well before the age-eight LDS standard for the point at which one develops accountability for actions, which strongly suggests that a variant identity isn't inherently sinful. But there are plenty of other biologically based conditions that while being technically natural would still be a bad idea to pursue with reckless abandon, so we'll continue the discussion with an investigation of whether or not this is something that belongs on that list also.
The claim that being trans is morally wrong hinges on the assumption that the sex an individual was assigned to at birth is the correct sex... but how do we know if that assignment was made correctly? Assigned sex is almost always determined based on external genitalia, assuming (correctly in many, but not all, cases) that internal sexual organs, chromosomes and brain match the external genitals. If a baby is born with ambiguous genitals then the parents and doctor might pursue investigation of internal organs and genetics; evaluation of the brain is a technology that it still in its infancy, and so the most practical tool available in that department is simply to ask the individual what gender they identify themselves as.
In the typical case ("Adam" or "Eve" in Veronica Drantz' terminology), everything matches up nicely and there's no question as to whether that person is male or female. So what do we do with the oddball case where it's not so simple? When there's a clear mismatch between the various indicators, which one controls? External genitals, internal gonads, DNA, or brain/identity? [I consider the evidence that self-identity is strongly tied to brain sex to be adequate to lump those together into one variable, although you're welcome to do your own research before jumping on that bandwagon.] If we consider it necessary to properly identify an individual's real or spiritual gender, how can that determination be made reasonably and accurately?
I think we can all agree that the external genitals (and secondary sex characteristics, which are created through a similar process later in life) cannot be considered as the definitive identifier of an individual's true gender in cases where other indicators are in conflict with this crude check. To claim that external appearance trumps all else would be to insist that those involuntary sex changes inflicted upon newborn infants change the individual's true nature... which is in direct conflict with both scientific and religious understanding of the nature of identity. Similarly, to claim that external appearance at birth is the end-all answer to how God intended the individual to be is a blatant denial of the well-documented occurrence of birth defects caused by neonatal exposure to man-made toxins.
Internal sexual organs have a higher correlation with genetic sex than the external appearance does, typically consisting of gonads that match the genetic sex and a hybrid of male and female characteristics at the interface with external organs that are in conflict with the genetic and gonadal sex. In that sense, arguments related to the internal organs would be a hybrid of the claims related to genetic sex and claims related to external appearance, with the respective validity of each being discussed elsewhere in this post.
That leaves genetic sex and brain sex / self identity as the remaining options for how we might go about conclusively determining the true gender of an individual. For those who believe in such things, it's generally agreed that an individual's spiritual essence becomes associated with the physical body sometime between conception and birth. If this event occurs at or soon after conception, then it would be reasonable to assume that the gender of the spirit matches the genetic sex of the body and that all other conflicts that might be present later are the direct result of the evils of the world. If the spirit enters the body at or soon before birth, then it would be reasonable to assume that the gender of the spirit matches the sex of the now-developed infant brain and that the self-perception expressed later in life are an expression of the individual's spiritual nature. But which of those is it? In answer to that last question, I cite Section 21.3.10 of "Handbook 2: Administering the Church" (for the non-LDS folks, this is one of the official documents that spell out how to handle practically every imaginable scenario that might come up for administration of LDS policies):
It is a fact that a child has life before birth. However, there is no direct revelation on when the spirit enters the body.And so all attempts to logically determine a one-size-fits-all formula for how to determine an individual's true gender go down in flames. If we believe that each individual has a true gender that is of a spiritual nature, then it would generally be morally ethical for them to behave and present in keeping with that spirit gender and morally objectionable to behave and present in a manner contrary to their spirit gender... but we can't even begin to assess which side of the binary would be appropriate for a given individual without first knowing the gender of their spirit, and there's no objective way to test or deduce what that spirit gender is for people who are born with a medically documentable intersex condition. [Note my use of "documentable" rather than "documented"... the intersex condition is there regardless of whether or not we're bright enough to go looking for it; discovery of an intersex condition merely changes our understanding of the situation, not the nature of the individual in question.]
So in the case of a trans person, is transition to life as one's identified gender a sinful denial of divine designation or an acceptable expression of one's true inner self? Some of my readers will find this to be a very difficult challenge, but it's time to recognize that the situation is nowhere near as simple as we might like it to be and admit "I don't know." Maybe transition is always wrong, maybe it's always right, maybe it's sometimes wrong and sometimes right depending on individual circumstances (I tend to lean towards that last possibility).
In my humble opinion, that's a matter than can only be resolved by personal revelation on a case-by-case basis... and in keeping with the principles of authority required for receiving of revelation, that knowledge is most likely going to be given first to the affected individual and as a secondary confirmation to family members, church leaders, and friends. Determination of individual gender is not "a matter that affects the whole Church" any more than the size and configuration of your genitals is, although Church policies related to individuals for whom gender and apparent sex do not align certainly would be. While certain individuals have had their non-apparent gender confirmed by the First Presidency, such revelation was not a broad Church-wide direction; it was a confirmation to appointed leaders that the impression the affected individual had previously received really was divine in nature. As to what place(s) trans and intersex people might be eligible for in God's kingdom (both here on Earth and in the next life), that's a question we eagerly await direction from the First Presidency on.