I don’t know about your hypothesis. My sister had terrible excema when she was an infant. The doctors kept my mother in the hospital for six weeks and sent her home with my grandmother. The excema was so bad that my grandmother used to cover her with a blanket so that people wouldn’t ask what was wrong with her. The doctor told my grandmother to put her on soy formula, take down the drapes, pull up the rugs, get rid of all wool and stuffed toys in the room and bathe her in cod liver oil (the water had too much chlorine). He said that if she did not follow his instructions the baby would have asthma by the time she was three and other food allergies. My grandmother followed the directions to the letter.
My sister was the only one of us that did not develop allergies, and she had beautiful skin.
Soy and peanuts are related and some allergies are caused by repeated exposure so it is a good place to start.
That does not mean that all kids fed soy will have peanut allergies later in life just that a higher persentage of them will.