Of course there are instances when science and medicine makes mistakes. Thalidomide, for instance: big mistake. But thalidomide was given to people with the intention to help them, when it was shown to harm them it was with drawn and everything done as it should be. That was medicine and science making a mistake, admitting it, and the same people working to help the situation.
What you have here is not one small study or a few drs saying that vaccines are the absolutely best way to keep our children safe and improve global health outcomes. You have many many years and thousands upon thousands of studies and drs and scientists. Pretty much all of them.
And up against them you have a few discredited studies, bad scientists, tinfoil conspiracy theorists, and some unqualified parents who don't know the science from a hole in the ground.
We need to treat these people in the same way we treat aids deniers, those who advise people not to take drugs for their HIV/AIDS because they firmly believe it all the be lies and they know better. They are on a par with those that preach that condoms aren't the way to stop HIV. The arguments put forward by the anti-vax brigade are chock full of outright lies, half truths, misunderstood science and twisted actual information.
We're not really all in the same position. Many non-vaxxers are not pro-safe children, they are pro-safe their own children and other peoples can go hang.
Yes, some of us make dif judgements than others. Some are right and others are wrong. Not all opinions are equal and not all decisions have the same outcome.