So I take it that a "few" people on this forum didn't pay much attention in biology lessons at school??
Nothing is completely safe - but frankly the risk of mild adverse reaction to a vaccine compared to the risk of serious illness?
examples
Vaccines are amongst the safest "drugs" that can be given to humans as they work with the immune system, whereas most other drugs disrupt or enhance a specific cellular process (which can have knock-on impacts on all the connected processes)
en.wikipedia.org
the MMR combination vaccination is safe.
Much of the modern anti-vaxxer nonsense can be traced back to the "con-man" Andrew Wakefield, who actually falsified data in his original paper (unlike UEA in the climate change debate)
en.wikipedia.org
And for balance - in the case of vaccines, the most worrying side effects are unanticipated immune responses - which are going to happen almost immediately (so don't require long-term studies in the same way) - which is different to the therapeutic drugs question
We must urgently develop measures to tackle the new coronavirus — but safety always comes first, says Shibo Jiang.
www.nature.com
As NOTN said - lots of people have not experienced a world with smallpox, endemic polio or other awful diseases that have been all but eradicated by vaccination.