Well, someone that believes vaccines cause autism or in flat Earth based on imperfect evidence, if they're being honest there should some more convincing, less imperfect evidence capable of changing their minds. Of course, we can certainly think of reasons why it wasn't as perfectly convincing as we initially thought, but I think anyone who starts changing the goalposts realizes they're on the back foot at this point.

After doing this two ore more times, you can easily make the argument that it's just simpler to abandon that model, or to suggest that perhaps they believe what they do not for empirical reasons, but for some other reasons (like being part of a community they like).