This is just smart people being dumb because they're science smart, but people dumb.
Firstly, you cannot reason someone out of a position they have not been reasoned into.
Secondly, people believe what they believe because it suits them to believe it. "I don't care about the science of vaccines, I am scared of injecting something into my body."
Thirdly, follow the money. Smoking might be bad for you, but making cigarettes is big business. With big social change comes big shifts in money. Thus coal ignores climate change, because to do otherwise is suicide.
Fourthly there's a trust problem. If you know your leader lies, or acts in bad faith, then by extension they all do [1]. If all leaders lie or act in bad faith then I no longer trust any leader. I assume you are telling me something to help you, not help me.
Ultimately the problem is not one of data (give the people data, and the tools (science) to interpret that data) but rather the implications of change, The abandonment of existing social circle, The financial loss, The improvement of others at my expense.
Science can't solve these issues, because they aren't science issues.
[1] if I assume the opposite, that only my leader lies, then clearly following him is stupid, and I am not stupid, qed.