In general, it seems that there has to be a slight distinction made between a diet during pregnancy and a mother's diet during breast feeding. Overall the available evidence is judged as 'not there' or 'too weak' to make any recommendation to avoid specific antigens.
Evidence is inadequate to advise women to avoid specific foods during pregnancy or breastfeeding to protect their children from allergic diseases like eczema and asthma.
We included five trials, involving 952 participants. Trials of mothers' avoidance of milk, eggs, and other potentially 'antigenic' foods during pregnancy or breastfeeding, or both, provide inadequate evidence about whether such avoidance helps prevent atopic eczema or asthma in the child. Women who avoided eating these foods gained significantly less weight during pregnancy in the one trial reporting on this outcome, raising the possibility of adverse nutritional effects on the mother or fetus. Finally, one small trial reported an inconclusive response of breastfed infants with atopic eczema when their mothers avoided consumption of cow milk and egg.
Prescription of an antigen avoidance diet to a high-risk woman during pregnancy is unlikely to reduce substantially her child's risk of atopic diseases, and such a diet may adversely affect maternal or fetal nutrition, or both. Prescription of an antigen avoidance diet to a high-risk woman during lactation may reduce her child's risk of developing atopic eczema, but better trials are needed.
Dietary antigen avoidance by lactating mothers of infants with atopic eczema may reduce the severity of the eczema, but larger trials are needed.
Kramer MS, Kakuma R.: "Maternal dietary antigen avoidance during pregnancy or lactation, or both, for preventing or treating atopic disease in the child." Cochrane Database of Systematic Reviews 2012, Issue 9. Art. No.: CD000133. DOI: 10.1002/14651858.CD000133.pub3
To the contrary, a few studies highlight a possiblly protective effect revealed by correlational outcomes in a prospective study:
Among mothers without P/TN (peanuts/tree nuts) allergy, higher peripregnancy consumption of P/TN was associated with lower risk of P/TN allergy in their offspring. Our study supports the hypothesis that early allergen exposure increases tolerance and lowers risk of childhood food allergy.
Frazier AL, Camargo CA Jr, Malspeis S, Willett WC, Young MC: "Prospective study of peripregnancy consumption of peanuts or tree nuts by mothers and the risk of peanut or tree nut allergy in their offspring.", JAMA Pediatr. 2014;168(2):156.
But that is not a universal:
Maternal CM avoidance was associated with lower levels of mucosal-specific IgA levels and the development of CMA in infants.
(CM = cow's milk; CMA = cow milk allergy)
Järvinen KM1, Westfall JE, Seppo MS, James AK, Tsuang AJ, Feustel PJ, Sampson HA, Berin C.: "Role of maternal elimination diets and human milk IgA in the development of cow's milk allergy in the infants.", Clin Exp Allergy. 2014 Jan;44(1):69-78. doi: 10.1111/cea.12228.
And if you then compare
High maternal consumption of milk products during pregnancy may protect children from developing CMA, especially in offspring of non-allergic mothers.
Tuokkola J et al.: "Maternal diet during pregnancy and lactation and cow's milk allergy in offspring.", Eur J Clin Nutr. 2016 May;70(5):554-9. doi: 10.1038/ejcn.2015.223. Epub 2016 Jan 13.
Then I conclude that we do not know anything certain about this –– but any avoidance scheme seems quite unfounded.
That is most unfortunate, as mothers were apparently quite shaken by 'scientific' and 'pseudo-scientific' in recent years:
In conclusion, all mothers in the present study restricted at least one type of food without scientific rationale while breastfeeding and more than a third of nursing mothers experienced difficulties with diet restriction. Nursing mothers should be educated on proper diet practices while being warned about unscientific approaches to diet restriction. In recent systematic review, education and emotional support by healthcare providers could enhance breastfeeding). We expect this study will give scientific basis for dietary recommendation to breastfeeding mothers and could promote a breastfeeding.
Goun Jeong et al.: "Maternal food restrictions during breastfeeding", Korean J Pediatr. 2017 Mar; 60(3): 70–76.
Published online 2017 Mar 27. doi: 10.3345/kjp.2017.60.3.70