First, I should clarify that you misinterpreted that chart. It doesn't say butter is bad. It lists fat sources which are tolerable, and according to the list, they are coconut oil, butter, beef tallow, and olive oil. (I wouldn't include olive oil on this list if you are dedicated to making this diet work well.) It wants you to avoid "seed oils", which are vegetable oils such as corn oil, soybean oil, canola oil, cottonseed oil, sunflower oil, safflower oil, etc—major sources of omega-6 fatty acids. It also mentions low-fat seafood being preferable over high-fat seafood. In other words, this chart is promoting a high ratio of saturated fat and low ratio of polyunsaturated fat.
Technically, commercial popcorn is probably not okay to eat on this diet, as it could contain vegetable oils. You would probably be forced to make it yourself, and the final nutritional value of such a snack is up to you.
Poultry is not listed, mainly because of the diets of commercial chickens. Those diets ensure their meat is fairly high in omega-6 fatty acids regardless of whether or not the chickens get to roam free. (Roaming free can improve the fatty acid ratios a little though.) Technically, even though eggs are listed on this chart, you could do even better if you avoid them too. In comparison to everything else on this chart, eggs are major sources of omega-6 fatty acids, but they are often included anyway because eggs have a wide range of nutrition. Ruminants are exceptions to the treatment of modern, commercial livestock, in the sense that the bacteria in their intestines turns much of the polyunsaturated fats into saturated fats.
Sometimes, I think coco-cola is listed in this context just to be rebellious against common thinking. I more or less follow this diet, but I don't drink coco-cola. However, I do not necessarily abstain from refined sugar around mealtime. Soft drinks are problematic even for followers of this diet, because high fructose corn syrup is considered less desirable than cane sugar (rightly so), and some drinks have added phosphorus. The allowance of refined sugar in this diet may give some pause, but that's because they don't yet understand that the main fat loss and fat prevention methods listed here are avoidance of polyunsaPost too long. Click here to view the full text.