Not vaccinating when everyone else is vaccinated is indeed a more advantageous game strategy, because there is no risk to die from the virus, and no risk to die from a mistake. The problem is that if enough people take that strategy, there will be no herd immunity and chance of dying from virus will become much larger than chance of dying from a mistake ever was.

The sentiment against anti-vaxxers is not simply because people do not empathise with the fears of anti-vaxxers, but because anti-vaxxers refuse to take the small risk everyone else is taking, and in doing so endanger other people who could not get vaccination because of other illness.