It's always cost-benefit. Relative risk of side effect directly relates to likelihood.
Risk of side effects vs benefit of vaccine.
I am not likely to take an HIV vaccine, since my personal chance of contracting HIV is incredibly low. So any side effect isn't "worth it" -- even a sore arm. But that doesn't mean I'm anti-vaccine.
I also don't wear a bullet proof vest around because it's too heavy ("side effect"). Does that mean I'm anti-bullet proof vest? No. But I would wear a bullet proof vest in a war zone -- even if it's heavy.
If there was a widespread small pox outbreak in the U.S., I'm certain more than 10% of physicians would take the vaccine. Does that mean they were lying before? No.