Even if the things you are claiming here were true - none of those things make the ideas of sex or "gender" fuzzy at all.
Intersexuality has nothing to do with transgenderism. They are people born with abnormalities that may make it more difficult to determine their sex - but they are still either male or female. No other option.
There isn't? Who makes the decision if someone is male or female? I might also point out, since you appear to claim this as part of your religious beliefs, Matthew 19:12, "For there are some eunuchs, which were so born from their mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive it, let him receive it."
Since Christ, just a few verses above, is talking about how at the beginning they were created "male and female," when talking about divorce, and continues into those that are eunuch's from their mother's womb, there is an implication that a "third sex" -- or at least those who don't fit into the male/female binary -- had come about due to the "fall."
I recently stumbled on to a YouTube video where a person with a successful YouTube channel where the creator talked of being born intersexed. The person was born with what looked like a female body and was raised as female. This YouTuber mentioned not being like other girls growing up. Then, when this person turned 16 it was realized that puberty had never started and so doctors were consulted. It was found, after a large number of tests, that this person was genetically male and that there were non-functioning (underdeveloped) testes in the person's body (which were removed due to threat of cancer), no internal female organs, etc. The necessary amount of hormones were not being created, since the organs that would create those hormones did not exist in that person's body. So, tell me, what sex (or gender) is this person? And if the gender this person is claiming now is different than what you decided, does that mean they are the "wrong gender?"
And to correct a possible mistake of yours, the best evidence is that transsexuals (at least those properly diagnosed) are a form of intersex. A number of animal studies have been done where, by manipulating the hormones at a critical stage of pre-natal development, that transsexual animals are created. Corresponding with this, it has been found in some tidal estuaries where large amounts of chemical pollutants, in particular fertilizers and pesticides that use estrogen as a major ingredient, there are a large number of animals (particularly birds) that exhibit transgender behavior, as the estrogens appear to be causing that transexual "birth defect."
Additionally, there have been a few studies of transsexuals where they do an autopsy on the brain and find that the brain structure aligns with the "sex" (or gender) the person claimed to be. In essence, they feel they are the opposite sex because of their brain and not because of "mental illness." It is also worth pointing out the most recent study particularly ensured the brains had not been influenced by the transsexual person taking hormones.
The best evidence is that transsexualism is a physical issue, not a mental one. The issue is that there are no real cures to this disease and the "cures" we have are wanting. Talk therapy and religion do not work well, they tend to lead to depression and shockingly high rates of suicide. Sex Reassignment Surgery (SRS) works better, and as pointed out have a higher "success" rate than many other types of surgery, but still isn't a "cure." As you point out, it makes the person appear as the gender they want to be (with varying degrees of success, it tends to be much more successful the earlier it is done) but does not actually make them that gender (no internal sexual organs, etc).
And while I stated that the earlier SRS is done, the better the results, that does not mean I support SRS on children. The professional standards have traditionally been that individuals must be 18 before any permanent, irreversible changes are made; though that has frequently been interpreted to mean surgery. One of the other, and perhaps the largest challenge, is how to accurately diagnose transsexualism; and the damage it can cause when misdiagnosed.
Whole cultures have had traditions about burning their children alive, sacrificing human hearts to demons, cannibalism - does that mean that these traditions are good or true and we should embrace them?
You seem to have missed the point. In all of those cases, those cultures have largely been condemned, even by the majority of cultures in the world in those times.
On the other hand, even you don't seem to condemn transsexuals, you just think they need help with their issues. The point is that these other cultures had their own way of "helping" these people and turned them into productive members of their culture, and even made them important positions in their culture. This did not cause perversion or for everyone to suddenly become transsexual. Maybe there are even things we could learn from them, that if we don't try to force people who feel trapped by their gender to conform to a particularly viewpoint, that we can "cure" them and not have them go through the issues of depression. I'll also note that the goal of therapy, at least traditionally, with transgendered individuals is to always do the minimum that can be done to make the person feel at peace; to not do surgery or hormones unless it has to be done to help the person become who they feel they have to be.
Hormonal imbalances can cause changes in our secondary and primary reproductive organs - but they do not change our sex.
You are free to do as you want - but I don't make a habit of lying to the people I love.
They need our love. They need the truth. They need the Lord Jesus Christ. To save them from this delusion. So, they can find peace.
Since you are LDS, I'll point out there are plenty of Mormon (or former Mormon) transsexuals who have not found the peace, that you claim they should find, through Christ alone. I'll also note that the position of the Mormon Church toward transsexuals has gotten more "liberal" over time. Last, I'll also state that I've heard stories (and I cannot verify them but heard them second hand from people who were in leadership positions -- Bishop or Stake President) of transsexuals who had SRS and were able, after interviews with General Authorities, to get endowed as their sex/gender after SRS.