Cheese, generally, contains a lot of fat and salt (as in natrium, I think in the USA it is called sodium). We're consuming too much natrium as it is.
There are other, cheaper methods of obtaining protein. Some of which are locally available. In Africa, for example, insects are used as local source of protein. They have a low Co2 footprint for a variety of reasons:
* Because a lack of transportation (locally available). Especially when compared to trademark protected cheeses such as Gorgonzola.
* Barely any land is used and it can be stacked, allowing more space for other land usage (generally that could be forests, or at least not adding to deforestation).
* No methane enters the air which directly affects Co2 emissions (which cows, generally the main animal used for cheese, do produce a lot).
Compare insects and cheese to avocados: for Europeans avocados are not locally grown, and the deforestation is a "far from my bed" show.