The DNA argument is debatable. There are chemistry signatures that differentiate male and female, and as you say, it's a slider and we have more and more control of that slider (we do now that ever before, and that will likely continue to increase), then we're at that point where it's not just a matter of dressing as the opposite sex, but going much further than that, which psychologically apparently is helpful for them.
It's a two way street. The people that have these inclinations didn't get to choose the gender-based societal roles that rule them, they're imposed on them.
We could easily make the same argument that religious people are mentally/emotionally imbalanced too, yet we protect their right to practice their religion. And as much as I expressed my dislike for organized religion in general, I've also expressed that I know first hand that it helps certain people, and if it works for them, and it doesn't affect me, what's the big deal?
The major difference between both is that people has practiced mysticism for centuries, while the ability for having a relatively effective trans-gender therapy is relatively new ( sexuality has existed for centuries too). One is fully embedded in traditionalism, the other isn't (yet anyways).
Realistically, if we're really looking at the slippery slope of allowing/accepting irrational behavior, that ship has sailed a long time ago.