you dont know what you are talking about
https://www.militarytimes.com/news/pentagon-congress/2021/06/17/troops-who-refused-anthrax-vaccine-paid-a-high-price/
In 2004, a court injunction halted the military’s mandatory vaccination program, declaring the previous six years of vaccine administration to be illegal.
The 2004 injunction was about the FDA approval process, not about whether the military could require vaccines overall. And even that injunction said that troops could refuse “unless the president ordered them”.
Once the FDA clarified approval, the injunction was lifted.
Troops can be ordered to do just about anything. An approved vaccine can easily be required.
This isn’t some kind of grey area. You join the military, you’ve signed over your life. You’re not in control any more.