Well first we need to characterise the problem correctly. Firstly, very broadly, living standards are improving on every continent except Africa. Infant mortality reducing, malnutrition reducing, life expectancy increasing (and for the Malthusian-minded among us, reproduction falling, often sharply).
Clearly there are areas on these continents that are continuing along lines of unsustainable production, and in many cases accelerating along those lines. To take one example, the cattle farming of Argentina has largely switched to the barn model in recent years, which is both horrible for the cows and horrible for the environment. Much of this beef is exported (although Argentines themselves eat a lot of it), but it doesn't go to Africa. For the majority of the people in sub-Saharan Africa whose living standards are falling while the rest of the world improves, meat is either not on the menu at all or it is a very rare luxury.
So the driver of change to ever less sustainable (and ever more cruel) production isn't the poor. It's the consumption habits of rich. Can we support 'loads of cheap meat for all'? Hard to see how. Can we move away from 'loads of (comparatively given wages) cheap meat for the rich'? Yes, and we'll need to, but not all meat production is equally unsustainable - pretty much all of British lamb production, for instance, is far more sustainable than, say, Argentinian beef.
What are the social and political means by which we produce a shift away from unsustainable practices? That's the real question here. And I think it's a cop-out to blame individual consumers. These are processes that need changing at the systemic level. I'm not going to have a go at a single mum on a limited budget opting for a multipack of chicken thighs at Lidl that can feed her whole family for a couple of quid. The danger as ever in this is that the burden and blame get placed on the wrong people - the poorer globally and the poorer locally - the people for whom 'choices' are in reality far more constrained.