We're not really in disagreement. Let me explain a bit more. Science is a process/methodology of exploring/understanding our natural world/natural phenomenon, Yes? And as such, there is good science, there is average science, and there is junk science. They're all under the same 'Science' umbrella.
>The science that supports the efficacy of vaccination is the data from the trials that shows a reduction in cases. This data is something anyone can understand with sufficient knowledge about probability and statistics.
Yes you have a bunch of numbers, but this doesn't tell you whether the study protocol was good, nor does it tell you about the qualitative aspects like how well the study protocol was adhered to, how tight the controls were, etc. Naturally, this is not a new problem, and we have various safeguards already in place at various levels. You also need a third party like say the FDA to audit and examine what was done.
>This data is something anyone can understand with sufficient knowledge about probability and statistics.
Yes, but that is not all. People need to understand how clinical trials are conducted, and how for e.g. efficacy numbers can't simply be used to trivially compare two vaccine candidates.