I'm not allergic to dairy, but I am however lactose intolerant but that didn't stop me or hurt my chances of joining. I honestly don't even think those factores were ever questioned in my enlistment process. Milk will tear my stomach up though! As long as you don't have asthma, or you don't wet the bed, major health or psychological problems like that will prevent you from joining the military or can be grounds for a discharge.
