1.) Right-leaning, free-market, anti-authoritarian types need to understand that climate change is a negative third party externality, and there isn't a free market economist that wouldn't agree that the state has a role to play in ameliorating that. Focus on the strategies you think are best suited for that role, such as carbon taxes.
2.) Left-leaning climate advocates need to realistically prioritize objectives according to their tenability and impact. Airplanes contribute 2% of greenhouse emissions, how about we don't start there. Energy production constitutes by far the largest impact, how about we focus energy there, and not to beat a dead horse, but also seriously advocate on behalf of nuclear. They also forget that the other half of the equation, carbon capture, is almost unilaterally popular. Focusing efforts on where the most leeway can be achieved is a much better solution, particularly since carbon capture is capable of handling carbon emissions of states unwilling to regulate their own outputs.
They also need to cool it with the catastrophizing. It is a bad strategy. All the opposition has to do is point out how incredibly off-base the predictions were in an An Inconvenient Truth, and they're done. Accurately identify where the feedback loops are that cause enormous leaps forward, and focus on those precise thresholds. Near linear progress in the way we've seen it creeping does not scare people, but that doesn't mean that we can just be wildly inaccurate with the predictions in order to scare people in to action.
Lastly, don't shoehorn in other political policies alongside climate propositions. Green New Deal, for example, is first and foremost a bundle of socialist policies using climate activism as a vehicle. If this is truly the greatest threat to humanity, decouple it from adjacent political policy.