I can't comment on the question of mouthing objects, but I can add something about exposure to nature. Recent evidence has found that allergies are often caused by children being raised in sterile environments. Consider the following article from 2010:
The study, by Guy Delespesse, a professor at the University of
Montréal Faculty of Medicine, linked the trend to the sterile
environment created by the cleaning habits of today.
Allergies can be caused by family history, air pollution, processed
foods, stress and smoking, but Prof Delespesse said a lack of bacteria
in the world around us may be the biggest factor.
"There is an inverse relationship between the level of hygiene and the
incidence of allergies and autoimmune diseases," says Prof Delespesse,
who is also director of the Laboratory for Allergy Research at the
University of Montréal. "The more sterile the environment a child
lives in, the higher the risk he or she will develop allergies or an
immune problem in their lifetime."
In 1980, 10 percent of the Western population suffered from allergies.
Today, it is 30 percent. In 2010, one out of 10 children is said to be
asthmatic and the mortality rate resulting from this affliction
increased 28 percent between 1980 and 1994.
But we have since gained a more nuanced understanding of the issue. The "old friends" hypothesis is that allergies are an immune system dysfunction, caused by a lack of exposure to the microbial biodiversity humans evolved alongside as grassland hunter gatherers. Thus, people living in developed nations (especially urban) have more allergies and less diverse gut bacteria, and inversely people living in less developed nations (especially rural) have less allergies and more diverse gut bacteria.
"The good news," says Professor Bloomfield "is that we aren't faced
with a stark choice between running the risk of infectious disease, or
suffering allergies and inflammatory diseases. The threat of
infectious disease is now rising because of antibiotic resistance,
global mobility and an ageing population, so good hygiene is even more
vital to all of us." [viii]
"How we can begin to reverse the trend in allergies and CID isn't yet
clear," says Professor Rook.[ix] "There are lots of ideas being
explored but relaxing hygiene won't reunite us with our Old Friends --
just expose us to new enemies like E. coli O104."
"One important thing we can do," says Professor Bloomfield, "is to
stop talking about 'being too clean' and get people thinking about how
we can safely reconnect with the right kind of dirt."
Furthermore, it seems likely that the "critical window" where exposure to microbial diversity is preventative is actually as early as the first 100 days of life. But it's not just about rolling about in a park, other sources of microbial diversity have a positive impact too. Like having a dog. Newborns from families with dogs were much less likely to develop certain allergies.
The bottom line is that if you want to give your child a life threatening allergy, then refusing to expose them to nature is probably a good way to achieve that. To help prevent this, exposure to nature in the first few months also appears to be a good idea.