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A lot of good people, who lack technical education, fall for the Flat Earth nonsense. They see how the media lie about some important things -- and that is definitely true, they do lie -- but then that leads them to start believing almost anyone who claims to be "exposing mainstream lies," not realizing that a large number of such people are nuts or grifters.
I do think that science-related education can help. In my former work as a broadcast engineer, I had to learn equations that would tell me how strong a radio signal would be at a given distance from the transmitting antenna. For the results to be accurate, these equations have to take distance, antenna gain, and transmitter power into account, of course -- but they also must include terms to account for the curvature of the Earth. The short version is that, if the Earth were flat, FM stations from Lisbon could be easily heard in New York City. Knowing that makes you immune to this particular kind of kookery.