The army is full of risk mitigation. Currently at most training posts (and others) to eat in the DFAC you have to wear a mask and gloves. I had to wear a reflective belt when I was deployed overseas in the broad daylight. They preach safety until your ears bleed.
And most importantly they want ensure a disease free fighting force. They force you to take any vaccination under the sun and believe me when I tell you that if they believed this vaccine benefits outweighed the problems they would be deploying it en masse to its soldiers. The fact they are making this optional tells you all you need to know.
Not a military pede so please correct me if I'm wrong, but my understanding is that is included on the list of rights you sign away when you join up.
No idea how they would discharge someone over a vaccination refusal. I'd think "other than honorable" is probably where most of those would land as that's what a lot of dudes who fail drug tests get. Again, speaking to something I only have second-hand knowledge of.
They might not be able to discharge a soldier for refusing to vaccinate, but rocking the boat puts you under the magnifying glass. Once you're sticking out like a sore thumb, everything you do will be scrutinized, you might get put on every task or detail, you might get put on every pee test for months.
This is what I was getting at. You stated it much more clearly than I did.