The only relevant question to me is: To what degree does allowing/disallowing transgender individuals to serve promote or detract from effectiveness?
The military doesn't exist primarily to demonstrate fairness. In fact it discriminates against lots of different kinds of people who don't fit a particular profile. Overweight people, those with a history of mental illness, the disabled, those above/below certain ages, etc. are not able to join for obvious reasons, because they would in large part reduce effectiveness in a number of ways we could go into.
To what degree should the military alter its standard operating procedures to accommodate a relative few individuals at the expense of its efficiency and effectiveness of the organization as a whole?
I support transgender rights. I dont view joining the military as a right. I do believe that a transgender person could carry a weapon and do the job of a soldier roughly as well as anyone else. But to what extent would their presence be a disruption to current protocols and culture would be the primary question. Not fairness.