In the military we have something called “unlimited liability”. It’s the main thing that separates us from civilians, and it ensures that the government can actually get things done with its military. It means we can be ordered into dangerous situations — situations which could cause almost certain death, and we have to follow those orders. If command wants you to be vaccinated against a certain disease because they believe you’re a liability if you don’t, you either get that vaccine or you reconsider your position in the military.
I also want to point out that one of the first things you do at boot camp is get a metric fuck ton of mandatory vaccines. If you opt to not receive them, well, bye-bye; have fun on the bus ride home. Anyone who is just now kicking up a fuss about mandatory vaccines is doing so entirely for political reasons.