I live in "the west" and I can contribute to change there. So I do. Try to change what you can change, instead of thinking about what you can't change and not doing anything.
problem is, unlike other issues that can have positive local impacts, the biggest downsides to climate change are global. doesn't really matter that as the US/EU our emissions have been flat for decades now if china and India are shooting up like crazy.
Sure, if you're talking per capita, US people emit more carbon dioxide but with your "even with 1/5th" and "the biggest polluter" it suggests you're thinking total not per capita.
The US were for a long time. But now it’s China. Although they already are the biggest producer of green energy world wide. They produce more green energy than all other countries combined. I don’t know if their strategy will drastically reduce their carbon emissions soon, for now they are still rising. In Europe and the US they are going down a while already (also because we moved a lot of our industry to china).