Is there such a thing as a hypoallergenic diet?

Yes. 95% of all food allergies are due to a few foods - milk & dairy, egg, wheat (barley, oat), soy, corn, seafood, peanuts, seeds & tree nuts. You can be allergic to others but most of the time you can assess whether you have a food allergy by cutting these foods completely out of your diet for 2-3 weeks. If you get better add 1 food back every few days to find the actual cause. Usually 1 or 2 foods.
Hypoallergenic diet. You will find tons of naturopathic diets claiming to be hypoallergenic, but the only true hypoallergenic diet is to find out what you are truly allergic too through seeing an allergist and only getting tested to foods that you have bad reactions with. There are tons of false positives. Elimination diets are the only true hypoallergenic diet. Elemental diets are very difficult to follow.