Science is not infallible but it's our best hope for progress.
Case in point, measles and other diseases that were on the decline but have resurged due to irrational fears that vaccines somehow cause harmful side effects.
The vaccine paranoia goes back to a single 1998 study that claimed a link between vaccines and autism. The study was later retracted and the authors' medical license revoked when it was revealed that his research was fraudulent and he was on the payroll of a group suing a vaccine-maker.
On the other hand, many, many studies have been conducted to independently verify the effectiveness and safety of vaccines. This repetition and reproducing of results is what makes science reliable.
So, don't put too much stock in a single study but if the results are repeated and confirmed by multiple studies then you can rely on the results. And, above all, don't pay any attention to actors and other charlatans who spread paranoia and misinformation. Trust the science! —Dr. Strangegloves