Some people think emotionally, not logically. Figuring that out took me way longer in life than it should have.
Logical thinkers will be able to do the risk/benefit analysis with “good enough” fidelity so long as data is available, so you don’t really have to worry about convincing them.
For the emotional thinkers, whom I am assuming have a large intersection with the people that believe misinformation (that assumption may need to be checked, but I ... just don’t have that data), perhaps we would have had better luck by pushing a message like “we are all soldiers in a war now, and soldiers take risks to protect each other.” Complete with an advertising campaign featuring a frontline combat veteran recounting how she walked out under enemy fire to rescue her comrades, and subtly or not-so-subtly shaming people who are unwilling to take tiny risks to protect their fellow soldier-citizens.