Not an anti-vaxxer, not by any means, just saying there are lots of things we think absolutely must have been tested to be completely safe when it turns out that it probably isn't as great for you as you'd like to have thought. That's all.
First, nothing is "completely safe." Everything has a limit beyond which it exceeds the capacity of a human to absorb it. On top of that, no injection or vaccination is ever 100% risk free. There is risk of infection, of allergens, of tainted products, etc. And there are also the risks of adverse side effects in some measure of the population.
People don't really understand statistics. They certainly don't understand a "one in a million" chance, as evinced by the profitability of the lottery. They also don't understand the consequences that result from these decisions.
I think a lot of that comes from a pile of numbers that people can't easily relate. Consider that a vaccine may have a 1:1,000,000 chance of causing the disease it was intended to prevent or causing a debilitating side effect. It may also have a 1:100 chance of causing an inconveniencing side effect. Its primary effect is to confer a 98% level of protection against a disease. The disease has a 20% chance of causing a debilitating condition. Unvaccinated people have a 10% chance of catching the disease. Herd immunity kicks in at an 80% immunization rate, and reduces my chance of getting the disease to 5%. Even though they're all based on probabilities, they're not even using the same units of measure for display. How does a layperson put all those numbers together to make a decision whether or not to immunize their child?
The flip answer is "they don't." Too many people lack the education needed to understand the numbers, to combine them, and to compare them; so they turn to experts. But how do they trust an expert? A few people are willing to claim to be an expert to drive their personal profit or agenda, instead of to serve the truth. And some people will cherry pick their list of experts to align with their agenda. It's the latter that are the corrupting influence, and those are the ones that need to be stopped.