> I dont think they have any obligation to save anyone else's life.
I reject this framing, the person here is not a passive observer in the first place, they are a participant with obligations.
Consider a pet dog: You aren't merely responsible if it bites someone after-the-fact, you also have a proactive obligation for a reasonable level of control and monitoring, so that your erratic property doesn't harm another person in the first place. That might mean blocking off where it can go with doors and fences, a muzzle, a leash in public, certified obedience training, etc.
Your body is like that dog: Both are biological property which can erratically move to harm others without your permission. In this case, the risk is it will start spewing tiny bioweapons at other people. As the owner, you again have some obligation to exert reasonable control and supervision over your property, whether that's quarantine, vaccines, masks, home tests, etc.
There are other options than vaccines, but one is still obligated to do something.