It is if there will be civil unrest, leading to the election of reactionary populist governments which roll back emission cuts.
Approaches to the problem that enrage a large portion of the citizenry are counterproductive. They won't work in a democracy, and most of the large polluters are democracies.
The French people are generally considered to be pretty left-wing (at least by outsiders) but they took to the streets as soon as the government raised fuel prices. Imagine how well that kind of policy would go down in Texas.
Poverty is therefore directly related to the question of solving climate change.