From my experiences I never felt unsafe with the transgender woman I worked with and I even shared a room with her. She married a man and so if we want to argue that toss I could have felt more subconscious sharing with a lesbian.
On the flip side I have personal experience of sexual assault in the military. It was at the time set up with shared ablutions between 20 mix sex, mostly male colleagues with only a flimsy white shower curtain to the shower cubicle. Thankfully they're gradually moving to en-suite accommodation.
The facts are that transgender people have been serving in the military for years without people getting het up about it. There are huge issues with sexual assault that have nothing to do with transgender folk.
As for mental health concerns, as I've stated before, the US military have a far wider issue and more troublesome psychiatric issues that they're happy to deploy troops with.