Vaccines are 99% safe. What we object to is that they're billed at 100% safe. And that prevents them from looking into how they could clean-up that last 1%.
If measles has a 1-in-1000 chance of killing those who contract it, and the vaccines has a 1-in-1000000 chance of killing those who get it, and there is a decent chance that you will encounter the virus then it's simple math to see that you should get the vaccine. But if the chances of encountering the virus are zero then you have to wonder if the 1-in-1000000 chance is worth taking. The fact the measles is (or was) practically eradicated is why the companies that produce the vaccines have to downplay, or outright deny, the small chance of side effects. This backfired when a few anecdotes about the genetically unlucky of the millions of kids who get vaccinated every year start circulating on the internet. "OMG! Vaccines are dangerous! They're all lying to us!".
We should step back, take a deep breath, be real about the issues, and fix just them. But I think we are going to discover the products were contaminated with retroviruses that can cause high fever in rare cases, the companies KNEW about it for years, but thought cleaning up the problem was too expensive, and are now in a situation where they can't acknowledge it without exposing themselves to the greatest scandal and viability the world has ever seen. It's gonna get messy.