I believe there are only two genders as well, but I still support homosexuality, and transgenderism. I think if a man feels like he will be happier as a woman, and if a woman feels like she will be happier as a man, then they should be able to change their gender.
However, some people do not transition completely and decide to stay as something between a man and a woman, that is something I do not think should be legal. If someone wants to change their gender, then they should have to transition completely, which includes hormone replacement therapy, sex reassignment surgery, and facial feminization surgery, for those transitioning from a man to a woman.
Having more than two genders or wanting to be something between a man and a woman is not psychologically healthy.
Those who were born as something between a man and a woman, I believe should have to transition to any one of the two genders, and I would support the government paying for their transition, though the government should not have to pay for the transition of someone who was born as either a man or a woman.
I should clarify that my position on this issue is not influenced by religion or conservatism, as I am neither religious nor conservative. I am a lifelong liberal, but I think that a lot of people who also identify as liberal are going too far and their actions could lead to societal collapse, which could then result in an ideological world war, and the world cannot survive another world war, since modern weaponry is too dangerous.