Climate change is incomparable to many of the so-called "problems" you may point to.
Of course, if you argue that there wouldn't be as much development and energy use under communism, then i agree - but that means the "problem" is not the economic system, but lifestyle and energy use. If people were willing to sacrifice their energy use - aka, no cars, no transport, no plastic products etc.
Under a non-capitalist system (at least from an anarchists perspective), the people affected would also be the ones to decide how much to emit -- and it's unlikely they would be as crazy about climate change.
(Not to mention that assuming "the lifestyle of today" where a small fraction of a percentage of the population does most of the consumption would be sustainable under anything other than capitalism seems like a mistake.)
The emissions from a coal plant somewhere across the ocean affects my weather here in California. In an anarchy, are you saying I would get a voice in the operation of that remote coal plant? How would that work, exactly?
The logistics of how to reach world-wide consensus, or at least something close to it, is an interesting question I don't have an answer to! Maybe coal plants would be practically impossible under anarchy, due to the consensus difficulties -- which one might argue is as it should be.
How would this be enforced? You wouldn't get any coal miners or other material providers to help you unless you can show your coal plant is truly something humanity at large either wants, or at least does not care about.