It can be dangerous, both for the believers and other people. Many terrorists, for instance, are huge believers in various conspiracy theories.

Even if I know this is pretty useless, I feel an urge to speak up if the belief is harmful for the person holding them. If you believe that homeopaty can cure cancer, and that every big pharma is trying to poison you, this can have quite big consequences.

However, if you believe that moon landings are fake or the earth is flat, I have a harder time to find a scenario where it can harm you, so I don't bother.

On a final note, in the 90's I was pretty convinced that Echelon was totally silly, and we know how it turned out. So I tend to be a bit more cautious on what is true or not.