Even if powered by green energy, AC increases overall temperatures in a city (the heat has to go somewhere). Not global warming, but definitely makes it more miserable.
https://www.epa.gov/snap/reducing-hydrofluorocarbon-hfc-use-...
Also we have to live with the fact now that the planet is significantly warmer now, and is getting warmer still. Even if we stop polluting now, there is already much damage done. Peoples life’s have been changed, and we will need to change our habits to stay healthy in this altered world. This includes more air conditioning systems in places that previously didn’t need them. Staying healthy is just as important as stopping the climate crisis.