Merely believing in something false is harmless, but once in a while humans actually act on their beliefs.

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.

If that belief leads you to assault (even just verbally) retail employees for requesting you follow basic hygiene principles in slowing the spread of a pandemic.

If it causes you to act in accordance with the false belief in ways that threaten someone's safety. For instance, you might shoot up Comet Pizza.

By refusing to follow the rules set by the medical authorities. Refusing to wear mask, not isolating when infected, etc...

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.