You've got this backwards. Both taking action on climate change and buying American are popular [1][2]. Furthermore I don't know of much evidence that suggests taking action on climate change will raise prices. But you are right about protectionism in that way. That's the biggest problem here.
In the abstract I see no reason that global trade should breakdown if a significant majority of people in the world can agree about labor standards, human rights standards, etc. In the specific, I believe this was one of the major original purposes of the UN, though unfortunately the world we live in remains one in which the abuses of great powers go unchecked because the cost of nuclear war is too high.
[1] https://www.pewresearch.org/science/2020/06/23/two-thirds-of...
[2] https://www.reuters.com/article/us-usa-economy-madeinusa-pol...