Poor people already eat less meat. On the other hand, climate change will make basic foods more expensive. I'm from India. I've seen the miseries caused when the price of rice or onions goes up. It becomes a major political issue. But if chicken becomes more expensive, no one blinks, because people don't eat that much of it anyway. Maybe some people in the cities grumble because prices at restaurants went up, but that's about it.

Your argument is like saying "Taxing Ferraris more will make life harder for poor people because it increases average transportation prices".