Your link is not relevant to this issue so I don't know what point you're trying to make.
To be clear I support vaccination. But patients should make their own decisions free of coercion based on informed consent with full knowledge of the risks on both sides. Don't presume to patronize them with spurious, bad faith comments about "P-hacking". Let's see the actual data.
And FWIW, if you want a more complete (but much less amusing) explainer on the subject, wikipedia always comes through: https://en.wikipedia.org/wiki/Data_dredging
For example, peanut allergies don't exist because most people don't have reactions to them. You absolutely can ask the question for if peanuts are good or bad for a subpopulation.
The alternative is just sticking your head in the sand.
I'm not sure why you're trying to derail the discussion by bringing up data dredging. That would only potentially be relevant as a possible criticism of the methodology in a particular study. So what's your point?
As always, xkcd explains it best: https://www.explainxkcd.com/wiki/index.php/882:_Significant