I think we're in a vulnerable space right now where in some ways the divisions that were exposed and heightened by the covid pandemic leave us less able to deal with another serious pandemic in the near term. Add in pandemic fatigue and it's even worse.
"When polls said only about half of all Americans would take a vaccine, I was saying herd immunity would take 70 to 75 percent. Then, when newer surveys said 60 percent or more would take it, I thought, “I can nudge this up a bit,” so I went to 80, 85." [0]
Lots of talk of "just so we can flatten the curve" turned into "so noone ever gets infected again". The role of NIH/NIAD in funding gain-of-function research. etc. etc.
There's no denying that plenty of people didn't believe things that the government said were actually true. The problem, of course, is that it is hard to tell which statements are lies and which statements are true.
[0] https://slate.com/technology/2021/07/noble-lies-covid-fauci-...
No, I think at this point, the best way to reduce the number of people who believe the government lies to them is to reduce the amount of lies that the government tells them.
A 50%+ lethal disease won't leave many survivors to say "it wasn't that bad, everyone overreacted!". The initial wave of conspiracy-minded folks won't have a great time to say the least.