This was already collated in that quillette article written by a previous guest of Bret's podcast (others have done the same over the past few months but it's all over the place in twitter threads)
The evidence that mRNA-based COVID-19 vaccines are safe, and that they work, is about as solid as medical evidence gets.
quillette.com
then bret did a podcast responding to it and this is the thread responding to that:
The most frustrating thing about it is how people like Bret just slot into a narrative. Most aren't defending him because they care about the details. So some people persist, throwing up claims of bad faith, seize on irrelevant details which is mostly just an excuse to avoid cognitive dissonance about the pre existing narrative. Part of the credulity is in general ignorance about subfields of biology and medicine. Bret has a degree in theoretical evolutionary biology, particularly fundamental mechanisms of selection and change which have very little to do with basic biology, virology, epidemiology, and he has not demonstrated basic knowledge of statistics to evaluate medical studies, let alone have an expert opinion. He's just a conduit for even more ignorant vaccine skepticism, cartoonish anti-institutional ideology, etc