If a patient is consenting to the change, they should be able to get it. However, there are some doctors who may not agree with it and doing so would be against their religious beliefs. In these cases, the doctors should be able to refuse to do the operation because it does not line up with their religion.
The key word there is "consenting." If an adult has given informed consent to a medical procedure, there is no reason why it shouldn't be performed. The reasons may come across as strange to others who are not involved, but one of the marks of a free society is that we tolerate behavior that we perceive as strange as long as it is not harmful to others or the society as a whole.
Why not? If the adult in question wants it, and the doctor is willing to perform it, who are we to tell them they cannot proceed? It's no one's business except the doctor and his or her patient, simple as that really. I personally may not wish for a sex change, but I won't begrudge those that do, different strokes for different folks you know? So yes, doctors should be allowed to change the sexual orientation of consenting patients, there's no reason they should not be.
Changing the sex of someone through hormone therapy and surgery may be a drastic medical procedure. However, if adults want to change their bodies in such a way, then doctors should be able to perform the necessary tasks. Sex change operations may be strange, weird and not mainstream medical practice. However, there is a need for such procedures and doctors should fill the niche.