They cannot be dishonorably discharged for refusing the vaccine. They can be administratively given a general discharge.
Depends on how the CO wants to play it. When it came to anthrax, they busted the Sgt one stripe at a time for refusing to obey a lawful order, not refusing to take a shot. That "lawful" order was given by SecNav. I didn't care about the shot. I DID care I was being ordered to take it by a suit that didn't have his sleeve rolled up setting the example.
“When bad men combine, the good must associate; else they will fall, one by one, an unpitied sacrifice in a contemptible struggle.” Edumnd Burke