This is likely related to the significant decrease in gut bacteria (of all kinds good and bad) on a low carbohydrate diet, and a corresponding decrease in intestinal permeability.

Another proposed mechanism is inadvertent calorie restriction, which is common on high protein diets (because protein is so satiating), and on diets with few foods (because eating the same thing is boring). The effects of fasting on autoimmune diseases are well documented. It's thought that calorie restriction may be sufficiently similar.