"The issue really is the certainty that the risks outweigh the benefits."
There are two considerations here:
One is that some diseases for which vaccines exist are not terribly scary - e.g. chicken pox - so the small risk of the vaccine is perceived to be not worth it. I have not vaccinated my DC for chicken pox. They both had it and are now immune for life. You can shout "Selfish! Selfish!" at me all you like but it won't change the fact that it was a perfectly valid choice.
Second is that the more people vaccinate in a community, the less likely it is for a child to get a disease. As herd immunity increases, the risk of not vaccinating decreases (yes, now you can shout "Selfish!"
). This is why there are quite a few Game Theory papers out there that mathematically show that it is impossible to eradicate a disease with voluntary vaccination programs.
"the selfishness of creating risk for others based on nothing more than feelings and irrational fears (irrational because they have no foundation in fact)"
It's not just feelings and irrational fears, though. Some (few) babies do react terribly to their first vaccines. Some (few) children do regress following vaccinations. These don't seem possible to diagnose before the vaccination.
"Like my fear of flying is irrational. People have died in planes. But the benefit to me of flying to somewhere (as opposed to the statistically greater risk of driving) is greater than the that tiny risk of crashing."
I think you might be confusing Probability with Risk.
Risk = Probability of something happening x Just how bad that something would be if it actually happened.
For example, I had two amniosyntheses in my two pregnancies despite everyone saying "But the risk of a miscarriage is so much bigger than the risk of a genetic problem!" which was a misrepresentation. The probability of a genetic disorder was much smaller than that of a miscarriage, but I wouldn't have minded miscarrying a fetus as an outcome as much as an incurable genetic condition in my baby so the risk of the amnios was actually more acceptable .
"Can we run society on unfounded ideas and irrational fears?"
I don't think this is a relevant question. Arguably the society is already running on unfounded ideas and irrational fears, at least if my Facebook feed is anything to go by.
"Or should we run then on fact and for the good of all?"
Dictatorship of the scientifically minded, in other words. I wouldn't mind it but some others might not be happy with this plan of yours.