I would have to know more about the living conditions and the military lifestyle to come to a firm conclusion about it. For example, do transwomen use female group showers on board a ship or at a military base? How do the biological women feel about that?
Honestly, I know practically nothing about the arrangements in the military, so I am guessing.
It seems most likely that in the relatively structured and disciplined world of the military those sorts of issues could easily be dealt with. What I could more easily see is folks like Chloe being quietly and surreptitiously sabotaged by transphobic coworkers and such. People who just don't like those ungodly weirdos and can get rid of them, particularly easy in the current Trump/Hegseth regime.
Just my guess, but I do have a clue about how bigots can get things done.
Tom