Expanding on my list in Communicating Climate Change ...
"Assume a lack of shared values and information, skepticism about methods and conclusions, and expect to face suspicion rather than assent."
Scientists and other scholars are often very badly ill-prepared to deal with the wild and wooly reality of communicating climate change and other contenious issues in the public sphere. This is partly because—adversarial and ill-tempered though they can be—academic research communities share foundational commitments to and conceptions of the nature of evidence and argument.
When scientists disagree about methods and conclusions, they do so within a shared ethical and epistemological framework laid by years of rigorous professional training. And they tend to forget that not everyone has those same commitments, those same assumptions about evidential and argumentative rigour producing critically tested conclusions.
Untrained lay people have a more informal and heuristic approach to evaluating evidence and drawing conclusions. And in the case of climate change, they operate in a media landscape rife with sources of denialist disinformation and propaganda, which are perfectly willing to claim that scientists and climate science are, well, disinformation and propaganda.
So when it comes to doing public outreach, start by checking your assumptions ... your epistemological assumptions.
Almost no one outside the scientific community understands the rigorous methodological and social norms that structure it. So, tell the story of science a bit. Don't just throw around numbers and charts. Give your audience a sense of the commitment, the effort, the history that's gone into the amazing accomplishment of figuring out how the world works! Don't leap too quickly to conclusions: bring people carefully along for the ride, setting the context and explicitly drawing conclusions from the facts (without, of course, dipping into condescension).
Moreover, the last few decades of politicization and polarization mean that many folks who aren't already on-side with the reality of climate change—and who are therefore a really important audience—are likely to be suspicious of everything you have to say, including your motives, your evidence, and your conclusions. Most of us aren't used to assuming that we face that kind of hostile interpretive audience, so take a third and a fourth look at how you deliver your message and how you take folks from A to B to C.
Having a sense of your audience is absolutely central for effective communication. In this case (and here I'm speaking as an academic and likely to my peers) it means attempting the difficult task of becoming aware of the axiomatic certainties that structure your world view and considering how to speak with people whose understanding of the world might be fundamentally different.