Id guess just the opposite actually. Look at bacteria for instance. They mutate when exposed to antibiotics. Develop defense mechanisms, etc. Why? because shit is killing them off and they need to adapt to thrive. Id guess the same logic would apply to viruses. Not saying its a valid reason to not get vaccinated though.
Yeah, I thought about that too...
But remember that with drug resistant bacteria usually evolve because they don't get hit with the full treatment. And they are a bit more adaptable (since they don't require a living host to reproduce).
As far as viruses go, they need to keep finding hosts. Usually ones of the same species. The more infected people available, the faster it can evolve. If you can eradicate the virus in 99.99% of the population, it decreases the chances.
Also remember that vaccinations themselves are not 100% completely effective. So if you do the responsible thing and have your kid vaccinated against something, an epidemic at school could still hit him/her.
People who refuse vaccinations for the worst childhood diseases are essentially social loafers. As long as 99% of the population are getting vaccines, they have nothing to worry about. But if everybody or even a good chunk of the population were to follow their lead... CHAOS.
Kind of like having a bunch of buddies move a billiard table. There is always that one guy that just pretends to lift. If there two of them, you are screwed.