I don't take my 2 month old children out to places where they could be exposed - people are gross and cough, sneeze and splutter over everything. I have more of an issue with those that expose others to disease this way.
I also don't take them to public pools until at least over 12 months and rarely if then.

ETA - and its not so rare that vaccinations fail. Every child I know that managed to catch chicken pox were vaccinated. I think the word "immunisation' give a false sense of security to people.