Refined carbohydrates are not a problem. Sugar, potatoes, properly prepared white flour, and white rice are excellent food choices. In fact they are superior choices to foods like whole grains and beans, which tend to have allergens and antinutrients like phytic acid and trypsin inhibitors.

Anyway, any apparent epidemiological advantages to avoiding animal products in the industrialized world come down to two things. 1) The meat is mostly garbage; you have to consider only grass fed. 2) People are eating large amounts of muscle meat to the exclusion of the organ meats and connective tissue. This results in a chronic excess of tryptophan and a major deficiency of glycine. Iron overload is also a problem with eating too much muscle meat. A diet of steaks and chicken breasts without eating the rest of the animals is totally unnatural.

Dairy doesn't have these problems of low quality meat and too much muscle meat. Vegetarian with high dairy intake is an excellent nutritional choice.