Politicians look at best at next term, CEOs look at next quarter. Climate changes took decades to manifest effects. And those 2 groups produce most news "worthy" messages. Journalism is quite close to being dead (with local reporting already being buried), as rephrasing PR statements is cheapest and fastest way to produce "content". Who is supposed to nudge public discourse in that direction, "influencers"?
Not sure, but I have heard that more than plenty in public discourse (NL / W-Eur) and even the repeated blatant lies about the 2015 wave of migration to be due to climate change.
It is difficult to have a reasonable discourse when starting with such overkill positions. The topic is way too nuanced. The civil war in Syria had many reasons, political, economic, religious, but also environmental.
Climate change massively increases the risk on water supply and harvesting yields, and if that risk manifests in a situation where people are already unhappy due to other reasons, it can be the trigger for large-scale reactions.
With all that having many factors, you'll rarely be able to point to one thing as "the" cause. That does not make it less relevant, though.