I think that nobody should be coerced to vaccinate, himself or his child. I vaccinated my child because I considered that it is better like this. However, each person should have the right to choose for himself, ideally after knowing the true known risks of vaccinating and not vaccinating.
There is this theory that people that refuses to vaccinate prevents the full eradication of many diseases. They say that refusal to vaccinate not only affect the people that decides this, but also the people that vaccinate themselves but are in the small percent of people where vaccine is not effective.
I say we should take this risk of having not-vaccinated people in society. Here are some arguments:
In the first place this should be done in the name of individual Liberty. Each totalitarian regime had his ideas on how individuals should be shaped and behave, in what God they should believe. Over time, each such approach proven to be wrong for some reasons. As long as people decide for themselves, individuals should be free to choose to not vaccinate.
It is not an argument that they will jeopardize the vaccinated people where the vaccine don't work. A similar argument would be that we should not use cars because it jeopardizes the pedestrians that chooses to not use a car in their life. We cannot avoid any side effect of other people's free actions, only the most direct ones.
You can argue that not vaccinated people can become ill without doing a mistake (except maybe "not vaccinating") and they will probably spread the disease to vaccinated people where the vaccine is not effective. Well... why was the vaccine not effective in the first place? If they cannot make it effective, how can we trust their assertion about the possibility of full eradication? What if the population not responding to vaccine is higher than the one who don't vaccinate, what will we do then? Should we test all people and quarantine the ones that are possible spreaders? You see that we are going to weird conclusions if we go in this direction.
People that vaccinate and are afraid that they might be still affected could take a blood test to check the vaccine reaction. This is less intrusive than coercing all others to vaccinate. What if you vaccinate and you are infected by someone also ineffectively vaccinated?
If we allow people to be coerced in what they allow to happen to their body, the road is open for any other violation of freedom.
Actually, we cannot be sure how small are the risks of vaccines. We clearly see the benefits in the reduction in poliomyelitis. We still see the people that were crippled for life when this vaccine was not available, for example the great violinist Itzhak Perlman. I don't know vaccinated people that were affected by poliomyelitis these days. There are clear advantages over risks here, but is it the same for any vaccine? Could it be that some genomes might respond very badly to some vaccines additives? We don't know for sure.
We know that a very small part of the population had severe allergy reactions on some vaccines. For some diseases the possible reactions are far more dangerous than the expected danger from the disease that is to be prevented. In the latest years there are vaccines for low risk diseases (viral diarrhea), that rarely have severe complications if correctly treated. Similar risks are true even for a trivial flu (influenza), you can even die if you have a too high fever. Fur such low risk diseases, usually on optional vaccine list, it might be less risky to not vaccinate. People that wants to be "early adopters" could do it, of course. It might be even recommended for people with severe immune problems, but it should not be mandatory. It's just to hard to calculate exactly the probabilities here.
I don't think the risk of vaccines that are validated by time is so high. We would have notice it by now. However, we cannot exclude possible side effects over time, like a higher susceptibility to autoimmune diseases and allergies. It is better to have a "control group" and be able to discriminate either there is a significant correlation with vaccination. We don't need to enforce the "control group", it is just a gratuitous advantage provided by people that decide not to vaccinate.
Let's not be so arrogant about what we learned about human immunity. Better revise each assumption, including the possible inconceivable risks in the way we vaccinate today.
The power of diversity
These people that might take higher risks for themselves by not vaccinating, might be the ones that will save our species one day. They might develop new adaptations to a future non-vaccinating diseases. We might learn then from them how to fight to that diseases.
We know, for example, that the 1918's "spanish" flu killed especially people with strong immunity system, unlike the usual flu that mostly affects the people having an weak immunity system. What if all people would have had a strong immunity system?
Likely, during human history, a lot of civilizations were almost destroyed because of diseases that affected the majority of individuals. Still, the humanity survived because of individuals that were different and were less affected. These individuals were initially less adapted to their environment but in time their mutation proved to be more valuable than the mainstream genome.
The strength of the human race stays in it's diversity. Any attempt to reduce this diversity is weakening the chance of long time survival of the human race. Are we really sure that full vaccinated people will be best adapted when a totally new disease will strike? We need all the chances to survive through diversity, especially as long as we don't have the full quarantine that can be provided by space colonization
It is OK with me for you to not vaccinate if you think it's better like this for you or your child. I would say it is also OK to try to convince people you care to vaccinate. Just don't try to make it mandatory, this is almost surely a mistake.