The equity ethics of a carbon tax is often a hotly debated part of the discussion. Many object to the idea of making energy more expensive, because they assume this would disproportionately affect the poor. But to my mind, this is clearly not the case. It's pretty simple math.
Poor people are more likely to have smaller homes or apartments, and are less likely to own cars. When they do own cars, they are more likely to drive a great deal less than their upper-income counterparts. Upper income people also travel more, and are more likely to do so by plane (though this is less a "1%" vs. the "99%" thing than a gradual increase up the income scale*). Nonetheless, the expenditure for energy may be a larger percentage of the income a household has, and at the lowest end of the spectrum, spending more on basic necessities may be a real financial strain.
But think about how a carbon tax works, if it's refunded 100%. Those who use the most spend disproportionately, due to their higher use, but everyone gets the same refund. For the average, "middle class" user of energy-- the person who lives in an average home, flies an average amount, drives and average amount, heats their house an average amount, etc.-- this means that the amount of new tax exactly equals the amount of refund. For a household that uses less than the average amount, the refund is actually larger than what is taxed.
So with the awareness that low income households use less energy in virtually all aspects of their lives, what's holding us back?
There's a lot of goal post shifting going on in this conversation. While it's completely reasonable to wonder what the effects of lowering carbon-intensive fuels will be for income distribution, you can see people who oppose climate action pulling wildly from both ends of the deck to cobble together an argument. For instance, over the weekend I had a conversation with Justin Katz after he grossly mischaracterized a Projo article on climate. One of his statements was that climate activism was in danger of sealing the position of the haves by reducing opportunities to exploit resources. This is not, in itself, a totally crazy hypothesis, as we saw above (though I think it's wrong). But here you can see him calling climate change activism a conspiracy to redistribute income to the have-nots.
Taxing carbon isn't a conspiracy to redistribute income, because the reward to the recipient of a refund is due to their having economized on energy use. However, it's clear that those who already economize the most are the least well off. So a carbon tax-and-refund policy would be a break-even for the middle class, and would help the poor, while helping us to avoid a serious future cataclysm that could affect everyone. Who could be against that?
*Just to give an example., I've only flown once, before my memory, as a baby. My mom just recently announced to me on the phone that she'd be flying to see family. This is only her second or third time in her entire lifetime (we weren't "poor" growing up, but were probably best described as borderline working-class/lower-middle class). But for upper-income households, flying can be a many-times-a-year event. This is an interesting synopsis of a study from Germany talking about that.