Suppose a restaurant employee believes that the requirement to wash hands before returning to work is a hoax by the soap companies in order to sell more soap. If the employee believes this but never acts on it, fine. But if they stop washing their hands before returning to work, that threatens public health.
A more extreme example of false beliefs causing great harm is the Holocaust that was caused by Nazis believing the Jews are part of a conspiracy to undermine Germany and were the cause of Germany's defeat in WW1.
False beliefs can cause a lot of harm to a lot of people in both personal level (not vaccinating your kids) and to the larger societal level.