It's a useless way to frame the issue. Environmentalism is an easy sell. It's much easier to get people to agree with socialism if you use climate change as part of your argument. But framing climate change as "first world vs third world" is just about the dumbest thing you can do because it puts everyone in the first world on the side of the corporations who are actively trying to downplay and obscure climate change.
If you make an actual, internationalist appeal for fighting climate change then you will have no problem getting people on your side. But framing the issue as "this one group of people is hogging all the resources and we need to stop them" will inevitably play into the hands of ecofascist rhetoric that views humanity as a virus on the earth.
Sorry for venting. Feel free to dunk on me in the comments
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This isn't an example of identity politics. This is an example of how vulgar materialist critiques can lead you down the wrong path. There is a genuine material contradiction between first and third world workers, but that contradiction in and of itself is not antagonistic. I was trying to explain how leaving your analysis at the level of mere contradictory vs non contradictory will end up failing the movement.