There isn't some 'one size fits all' fix. People, regardless of their science literacy, like easy answers and explaining climate change is all but that. You can (and should) still find reasons why people doubt, and even though you'll often find shit that boils down to "teachers spent years calling me an idiot for expressing individual thought, but had nothing but praise for those regurgitators (who are now those so-called 'experts')" it's still worthwhile to recognize their reasons first and not expect change overnight. Some will ponder an argument like "if you're so opposed to citing sources, why are you regurgitating this podcast? can't you explain it in your words?" others will think you've been indoctrinated beyond hope. You could very well be the first person who listens to them, and some people are so accustomed to being dismissed they won't even accept you could be genuine. So, yeah, pick your battles and treat them as people rather than stereotypes. That's so pointlessly general I'm gonna high-five my maths degree. Me? I thought the above about humanities verbatim, because here I was, a 14-year-old with buncha stories published in a national magazine and some old bag kept telling me I must not have a soul for not liking a book where literal trees had more character development than all the *gonists combined. I didn't need to be traumatized to change opinion, just experience positive feedback and interact with, you know, people who don't immediately equate "I didn't think of this" or "I didn't think of it that way" with "it must be wrong. "
You're absolutely right. On reflection, I think part of the problem is that the kind of disagreements I'm referring lately to have been in passing, and so there hasn't been as much of an opportunity for proper engagement and discussion of the kind you're referring to.