The problem starts when people's widespread incorrectness poses an actual existential threat to humanity in the long run. Then, we can't afford not to try to convince them, no matter how vain the hope of succeeding.

See: vaccines, climate change, guns, healthcare. People's stances on these are literally resulting in avoidable deaths. Thus, I will never stop trying to reach people. Call me an optimist, but I have to believe it's worth it.