The similarities lie in who does the deciding, diagnosing and curing. Both homosexuals and transgender people have existed historically before psychiatrists were invented. They were accepted or not. Among some native american tribes it was not unusual for biological women to be warriors and biological men to fill women's roles, so transgender individuals taking part in battles is not a new idea.
Trans people already do serve in the military, Obama lifted the ban (to win democrat votes) at the end of 2016 & a few thousand troops came out as being unsure which bathroom to pee in.
Serving trans troops won't be booted out. Just no more new admissions. Which is sensible.
If I do the hoovering & washing up, wear a dress & makeup while I do it, It won't make me a woman.
Nor if I have surgery, I'll still be a man, only, mutilated ....so I won't be able to do the housework for sometime after.....& I'll need to keep taking hormones & have counselling for the rest of my life.
Trans people have a high instance of mental health issues, depression, anxiety etc, both pre & post op.
The military isn't the place for bizarre & expensive liberal social experiment.