Yes, I believe the evidence that vaccinations (what’s with the scare quotes, anyway?) protect children from diseases. The fact that we live longer, healthier lives than at any time in human history suggests we’re doing plenty of things right.
Anyone who has doubts about vaccinations should simply ask someone like me, who lived through the 40s and 50s as a child, what it was like every summer when polio season rolled around. The fear was palpable and all parents lived in terror that their child would come down with polio. Thanks to modern vaccines polio is no longer feared every summer as it was only about 55 years ago.
There were very few vaccinations available when I was a child and most of us came down with measles, whooping cough, mumps and other diseases. We did have chicken pox vaccinations and I am glad we did. As soon as the polio vaccine came out, I made sure I was vaccinated and then again when I went into the army, was vaccinated for it.