If you have a male body but think it should be female, that is none of our business. On the other hand, you make it our business by demanding that we pay for your sex-change surgery and/or the medical care and hormone therapy that will follow it for the rest of your life. There is no "right" to serve in the military. Applicants have been denied entry to military service for as long as there have been militaries. Medical, legal, marital status, etc., are or have been discriminators.
We don't know what causes a person to believe s/he was "born with the wrong body," but the cause is irrelevant to whether s/he should be allowed to enter the US military, or to take steps to change that body once admitted.
THE purpose of the military is to "kill people and break things." All other functions are all other functions are incidental. So, whether you are blind, were born without arms, have asthma, are diagnosed with bi-polar disorder, use heroin, have a congenital heart defect, think you're supposed to have a penis and just were't born with one, etc., you should not be admitted to the US military. It's not personal. It's not a matter of morals or ethics. It's functional.
Note: We are keenly aware that underlying the publicly stated reasons for the demand that transsexuals be allowed military service is the never-ending campaign to "fundamentally transform" America and tear down it's institutions and traditions in the name of "social justice." Changes may be beneficial or even necessary, but must not be pursued with a myopic disregard for facts, rational thought and consequences.