People don't distrust science because evidence base is changing but because human (non)experts use a low quality information to overstate opinions make absolutist pronouncement. Even a top Doc-scientist like Fauci wasn't immune. https://www.medpagetoday.com/blogs/vinay-prasad/90445

In that case , perhaps it is better to present facts on table rather and tone down certainty of opinions. As if statements come from Authorities, it tends to discredit science. Check out this statement from WHO. https://twitter.com/WHOWPRO/status/1243171683067777024?s=20

Eg. Much of science/epidemiology in COVID has been fluid (variants, Reinfections,Drug trials, Vaccine side effects). In that case, it helps to use terms like likely/unlikely and quality of evidence ,when we r tweeting rather than absolutist pronouncements.

When we use terms like "proven no benefit", " treatment bites the dust" ,"awesome benefit","miracle" from low quality/equivocal trials expect rightly to be bashed. On an average non experts more likely to use such terms than experts.

For a normal person reading such information , always try to ask what is magnitude of benefit/harm and is the quality (level) of information (evidence)definitive

Many COVID Treatments(Steroids,Remdesivir, Tocilizumab, Anticoagulation,Plasma, Monoclonal Antibodies) have varying benefits/futility depending on the stage of illness of Patient. Beware the Doctor,who gives an absolute opinion of drug

Example : Steroids can be dangerous in non hypoxic Patients, Remdesivir is useless in Ventilated Patients, Therapeutic Anticoagulation is beneficial in moderate severity patients while harmful in ICU patients .

Since it is COVID Time , I also try to convey to my Patients, quality of evidence and magnitude of benefit in their given "stage of illness" whenever I use costly/experimental/potentially harmful drugs without definite data.

One of the reasons I stopped , frequent COVID pontification on my twitter TL, is because quality of information/evidence was flimsy-modest in most cases and yet
I was giving opinions based on that which might be misleading my followers.

I must have done that quite a few times, and I will try to delete those tweets where I am not clear ,but I realise that damage is done.
Less stridency in "tone" might lead to less popular influence,but u sleep peacefully.