I think these two things are in conflict. Drastic action on the climate will almost certainly make most people's lives harder (at least in the short term) and will probably be tougher on the poor than the rich - for examples food price increases due to higher energy costs. Once you get down to the nuts and bolts of the changes needed, it's a tough sell to those already struggling.
If you include all the externalities, fossils fuels are the most expensive, not the least expensive, of the alternatives we have today.
> Drastic action on the climate will almost certainly make most people's lives harder
The human body cools itself by evaporation of sweat. This mechanism stops working at 95 degrees F at 100% humidity, or at 115 degrees with 50% humidity. Last summer in southern Indiana, where I live, we have a week of over 100 degrees/50% humidity.
Recall, if you have a temperature of 103 degrees, they recommend you see a doctor immediately. Over 108 degrees and you risk brain damage.
And currently the world is warming at the rate of just over 1/3 of a degree per decade. Drastic action? The most drastic thing we could be doing is nothing.
Solar is already cheaper than coal, and the price of solar panels is following a Moore's law like curve. Wind farms aren't far behind, and they've already saved Texas's bacon a couple of times.
It doesn't matter how many social media sites they shut down, kids are going to be depressed because nobody seems to take the problems their generation are going to face seriously.
You might also say that past increases in economic inequality have come from other factors, so you might say we have headroom to roll back those to compensate for the climate crisis caused effects.
(Also as the poor are even now hit hardst by global heating, there's definitely a moral responsibility for the rich to do much more)