They’re the bane of every helicopter mom chauffeuring her kids to soccer practice. Little Auden can’t even look at a peanut without going into anaphylactic shock, and poor Phoebe gets hives from anything casting a shadow. Welp, if they ever need a bone marrow transplant then life’s going to become even more complicated.
There have been anecdotal reports in the past of people gaining new allergies from transplants of hematopoietic stem cells. These are the cells found in bone marrow, creating blood in our bodies. Since 1968 there’s been a consensus among doctors that bone marrow transplants can help people with weak, or compromised, immune systems by boosting the immune response.  An allergy is a damaging immune response to a substance most people find benign. It makes sense that bone marrow transplants, and newly strengthened immune systems, could transmit allergies but reports have been anecdotal at best.
For example, in 2010 a leukemia patient received a bone marrow transplant from someone with asthma, nut and fish allergies, in addition to hypersensitivity to dog and cat hair. Almost two years after the procedure, the patient developed an allergy to dogs after breaking out in hives after being licked by a dog. The case study notes the bone marrow helped develop an allergy in someone who was already predisposed to being allergic to animals since the patient was still able to eat nuts and fish. So why not inherit all of the allergies instead of just one? 
As the refrain goes, anecdotes aren’t data regardless of how many you have. But when there’s smoke, there’s fire and Natalie Garzorz and a few of her colleagues have proven the link between bone marrow transplants and acquiring allergies.  A patient who’s never had any issues eating kiwi fruit, acquired the allergy from a transplant of his sister’s bone marrow. Using fluorescence in situ hybridisation (FISH) to detect the origin of white blood cells, they incubated T cells with kiwi extract, discovering the white blood cells originated from his sister and her marrow.
Which raises the question; Could allergies be cured with bone marrow transplants? Might this be the first step in proving the basis for personality changes in organ transplant patients? And is this response an atavism of our planarian-esque forebears, where eating our peers conveys their memories?
Hematopoietic Stem-Cell Transplantation for the Treatment of Severe Combined Immunodeficiency – http://www.nejm.org/doi/full/10.1056/nejm199902183400703
Allergy transfer with hematopoietic cell transplantation from an unrelated donor – http://www.nature.com/bmt/journal/v46/n4/full/bmt2010150a.html
Newly acquired kiwi fruit allergy after bone marrow transplantation from a kiwi-allergic donor. – http://www.ncbi.nlm.nih.gov/pubmed/26990607