Barring an active epidemic, a person should be allowed to refuse vaccination for themselves and those they are responsible for and to not be punished by society.
That person will come into contact with people who cannot be safely vaccinated (those with compromised immune systems, young, elderly etc) who are most at risk for the diseases. And as such the person can be a carrier.
Everyone who can be vaccinated should be vaccinated to maintain Herd Immunity
The way vaccines work is mainly through herd immunity. No vaccine is 100% effective, but if the people around someone who is infected are vaccinated, the chance of it spreading to others is minimized. This is what stops epidemics before they happen.
This compromises people who are heavily at risk, such as people with AIDS, the elderly, and the very young. Because relationship webs grow exponentially, there is a sharp rise in cases even during a small decrease in vaccination rate.
This decision doesn't just involve himself, he's putting a lot of other lives at risk. The anti vaccine argument is nothing but ignorant. People don't have the right to make decision that put other people at risk. If I have Ebola, I don't have the right to just walk out the hospital.
Forcing vaccination reduces individual liberty, which constitutes a form of diversity with evolutionary and ecosystem implications. This reduces the agility of the system to withstand poor decisions. A vaccination that turns bad could kill a high percentage of people. Imposed vaccination? 100%.