I don't disagree, but I feel like you're understating it. The reason people don't trust "authority" is because they can't always tell when they're trustworthy, and the more disconnected from their "authority" figures they are, the less they are able to figure it out. So when public health officials, the same public health officials that told us to stay home, close our shops, give up our incomes and livelihoods and stability contradict themselves, they lose trust, and let's be honest,
rightfully so.
It is one thing for us as laymen to discuss the efficacy of masks, staying at home, shutting down the economy, not partaking in the activities we used to enjoy and so on. It is an entirely different thing for a person in some kind of authority, like "public health", where your primary domain of expertise is communicable diseases to step out of their lane (which is communicable diseases) and say despite the supposedly high risk of death and bodily destruction that an apolitical virus with neither vices nor virtues nor policy positions can wreck, it is entirely okay to go out and protest something, but only if it is something that "we in authority" currently agree is worth protesting. This is, by the way, not long after the 9th Circuit said allowing Churches to reopen (even with limitations) would make the Constitution into a suicide pact.
People don't trust authority because authority doesn't want to stay in its own lane. Take Anthony Fauci, he has done a remarkable job staying out of the fray as much as possible and simply acting as an advisor to the President and to the people, and people trusted him even when they wanted to imagine their own politics on him. As a civil servant, absolute standout guy, and he's now considered one of the most trusted medical professionals in the country because he stays in his lane, meaning he allows his politics to take a backseat (not even the backseat, it's back in the trunk) to his job and Office (Director of the National Institute of Allergy and Infectious Diseases).
Forgive me, I went on a small rant, but to conclude, when you have lying in the first instance and not staying in your lane in the second, one of the effects is going to be a loss of credibility, and that's both just and understandable. Choices have consequences, and that includes lying, and that includes using your unelected Office for activist purposes. Even when you're right about something, up to and including the efficacy of masks, you've already lost credibility, and in the case of masks, you've already directly contradicted yourself. (I mean "you" as in public health officials recently, not you specifically my fellow HN).