There is a lot of data out there that shows that kids who are not exposed to certain molecules such as those found in peanuts that they have a higher rate of allergens towards peanuts. there's a theory going around in the medical community that the lack of exposure to these allergens is a large determining factor in developing allergies. I'm on a mobile device so I can't look it up easily but you can search Google Scholar to find a good answer.

There was a nice paper that was reviewed in my journal club a couple of weeks ago about children who have allergies diagnosed at a pediatric age. it was a prospective study that took kids who had known allergies against peanuts and kids who did not have allergies against peanuts. the study separated each group to having a peanut diet and a peanut free diet. in the group of kids who originally did not have allergies those who had a peanut based diet, which meant had some exposure to peanuts on a daily basis, had a statistically significant less chance of having allergies I believe the number was 1 or 2 percent. and the kids who did not have allergies who had a peanut free diet an astounding 8 or 11 percent on aledge testing was allergic to peanuts.

In the population that was known to already have a allergy against peanuts the kids who had a peanut free diet almost all had a peanut allergy whereas those who were exposed to a peanut diet daily had something like 5 to 10 percent peanut allergies present.

This idea that being overly clean, feeding your child an unnecessary diet I ve gluten free peanut free excetera is actually detrimental to the development of a child. of course the data to support this is weak and at the time controversial but it is sparking a good discussion amongst the medical community. all of my colleagues, doctors that I work with are exposing their children to a regular diet and actually trying not to over clean things. if a couple of Cheerios fall on the floor then let them eat them