As far as the covid vaccine , I've seen too much evidence of people dying from stuff that was almost nonexistent in the recent past . Other vaccines , well I've seen evidence of problems such as autism that were a lot less prevalent before many of them were in common usage . Not any "scientific evidence" , just empirical evidence of a possible causal link . Snag
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In medicine it's extremely difficult and EXPEN$IVE to disprove an alleged cause and effect, especially a rare one, so the limited funding mostly goes to more productive efforts. That's why so many fad diets can persist. The COVID vaccine certainly does have a bad effect on some people, my sister for instance, but I believe without proof that her strong immune response was the culprit and the disease would have been much worse.
Here is an example of the uncertainty:
A possible cause the study didn't mention checking for is the high temperature breakdown products of fats etc, as in rare, medium or well done. The prof warned us about carcinogenic PAHs (tar, char) in Chemistry class in the 1960's, and since then I've cook meat at lower temperature.
Beware of studies that find what they were paid to look for. Researchers who don't may risk unemployment.