No, none of them has a right to decline this shot. They are property of the US Government.
Nothing astounding about it. It's an experimental treatment, with almost zero testing done to it. Legally, they can't force a single person to get the injection. Furthermore, contrary to what you think, service members are not mindless automatons. They have every right to decline illegal orders. In fact, unless things have changed since I was in, they have a duty to question and deny such orders.
If you think a service member can refuse a shot that he is ordered to get, you’re deluded.