When measuring negligence based on attempted mitigations taken to prevent harm or death of others, antivax would likely be considered extremely negligent, based on little to no efforts taken to reduce risk to others, or even intentional actions that purposefully increased risk.
Saying the virus kills and not the carrier/spreaders is like saying the car killed the person it hit, not the driver of the car. If you want to drive around your body with a deadly and extremely contagious disease, without mitigations, be careful who you crash into.
No one is forcibly injecting anyone, just society limiting access of those who do not care to limit their potential harm.