Ask the guy arrested after firing off a round in Comet Pizza. Yes, there are crazies out there who will act on fake news and become a danger to others and themselves. Plus there’s a general danger in getting your worldview from fiction you take as truth: cf. Don Quixote.
Basically fake news is dangerous for the same reason a fake map is dangerous: both are unreliable guides to reality and can lead to making serious errors. Reliable guides are consistent with reality.