Dairy Intolerance Symptoms. Intolerance to dairy foods can stem from a negative reaction to lactose or to milk proteins. Lactose intolerance is a digestive disorder in which you lack sufficient lactase, the enzyme that breaks down lactose in your gut. Symptoms of abdominal cramps, bloating, gas and diarrhea shortly after consuming milk products might indicate an intolerance to this milk sugar. Milk protein allergy, on the other hand, is an immune disorder that causes you to produce antibodies against the proteins in milk. Symptoms can include digestive upset, skin rash and breathing problems, and a severe allergy can cause life-threatening anaphylaxis.