With my eldest, there was a big debate around MMR. My mother scared the bejesus out of me with her views....we didn't get many vaccinations as children as she didn't believe in them.
I tried to talk to GP but they were not helpful. I wanted to research single vaccines, they wouldn't help or recommend reputable places. So I left it.
I did tonnes of research. In summary. Everything carries a risk. The risk of getting the diseases and dying from them were far higher than the risk of vaccine damage in a healthy child.
I finally got DS vaccinated before school, when I realised I was in charge, not my mother.
All kids since vaccinated sooner rather than later. Not just for my children, but for the greater good of society, especially those more vulnerable with underlying conditions that make vaccinations for them impossible or at higher risk of complications.
Like a lot of things, we must have more transparency when we ask or question medicine or vaccinations. We should be allowed to question. It wasn't that long ago, we had mercury in vaccines. And of course, thalidomide was deemed safe 
And the easiest way to help people understand is risk levels. So 1 in million is vaccine related injury, or 1 in 100 if you get measles and develop complications (as an example, not real stats).
Very very very grateful that we pop along to the docs to protect our children for free.