That's a pretty quickly self-limiting population. As is the Antivax community, though the flareups of forgotten diseases will continue for a few more cycles before this group dies out naturally - So long as we don't fan the flames by actually persecuting them. More than a few will die of disease, most will learn better from seeing the results of their actions.
A significant portion of that population will develop natural immunity (mostly by natural selection) and will be the one to survive when at some point centralized supply chain is exausted out of resources and all the viruses that they had vaccines for come back with a bang.
