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No, but you should weight them appropriately.
And unfortunately in the current circumstances there is a lot of "trusting what you are told" to be done. You (and I) are not, as far as I am aware virologists, epidemiologists, or anything else that gives us a unique view on this. We have experts who have studied and worked in this field for decades and we have to accept that their knowledge is more detailed than ours.
Of course you should not be unquestioning, there are very real and difficult questions about whether the courses of action that we are taking are sensible. There are definitely questions to be asked about speed of vaccination, what level of death is "acceptable ,about whether vaccinating the world's population is necessary, achievable etc
This "open minded/closed minded" talk is phenomenally unhelpful in my opinion.
Should people be "mindful" of what they shove in their arm? Of course they should, but let's try and go off reasonable datasets, not "I know a nurse and they think..."