I am unsure about what to think about this. I have three kids all with food allergies. I have been told that their food allergies are genetic. I breastfed all of my kids. My first son had signs of allergies from infancy. He would sneeze and get hay fever looking eyes, all red and itchy, every time he nursed…from newborn. I was eating all of the major allergens and they seemed to affect him through my breastmilk. The first time he had a major reaction was when I first introduced solid food (really watery rice cereal mixed with formula.) I had been feeding him the rice cereal for about 2 weeks with no major symptoms, but one day I was not at home and had no expressed breastmilk to mix with the cereal so I mixed it with formula. He was just over four months old and the first spoonful touched his lips and he started screaming like it was burning him. He quick turned his head and it got on his cheek and then turned to big red blotches with white little hives on his cheek. He continued crying and trying to use his arm to wipe off his cheek and the red blotches and hives then spread to his arm.
It took until he was nine months old before I could get my pediatrician to refer us the the pediatric allergy specialist. After the visit, the did the prick tests on his back, we found out he was allergic to milk, eggs and peanuts. He is now 16 years old and still has anaphylactic results when accidentally exposed to milk products. (His throat and tongue itch & swell.)
When I was pregnant with my second child, I was encouraged to avoid those foods my son was allergic to until I was done breastfeeding. But instead of milk, eggs, and peanuts, my second son is allergic to beef, pork, and chicken! My daughter (our youngest) is allergic to beef, pork, milk, peanuts… I had decided not to avoid any foods while pregnant and breastfeeding with her.
All of my kids got allergy tested at young ages and not sure if early introduction to ANY specific food would have changed their allergies now! I now just manage their diets with healthy, organic, whole foods that don’t trigger their allergies.

I would not personally give this before six months (I never pumped anyway so I couldn’t have) but would implement when introducing solid foods for the first time anyway. In the past, parents would not have avoided these foods at all so babies would have had regular early exposure.