> Normal people don't care about climate

This is not true, it's fossil fuel propaganda that has been very successful. The overwhelming majority of people are concerned about the climate but assume that they are in the minority. See https://ourworldindata.org/climate-change-support for example.

"Fight pollution" is the old approach, it doesn't work as well because greenhouse gases are generally invisible and cause no noticeable short-term impacts, and because in the US the industry has been successful in distorting the law such that greenhouse gases do not legally count as pollutants.