First World societies affect the environment to a great degree. They affect the environment much more than poorer societies do. It is true that people in poorer societies are more likely to do things like cutting down or burning forests, but people in rich societies still have a greater impact because of all the resources that they consume.
People in rich societies consume tremendous amounts of resources compared to people in poorer societies. According to the pie graph in the link below, the richest 20% of the people in the world do 76.6% of the world’s consumption. The text in the link says, for example, that the average American uses as much energy as 6 Mexicans or 307 Tanzanians. This is true because of all the goods we consume and all the energy we use. We use energy to drive our cars. We use energy to charge all of our electronic devices. We use energy to heat and cool our homes. We consume energy indirectly when we order packages that get delivered by UPS. We also use tremendous amounts of resources. We eat a lot of food and, in particular, we eat a lot of animal products. This means that we are responsible for all the resources consumed by the animals we eat.
All of this adds up to a lot of environmental impact. In particular, all the energy that we use contributes to our carbon footprint and to global warming. Demand for things like beef can help lead to deforestation in poorer countries who cut down their forests to graze cattle or to produce food for cattle.
In short, First World countries have a tremendous impact on the environment because they consume so many resources (energy and otherwise) that they end up affecting the environment much more than poorer countries do.