Without following this subject closely and admitting without ever really looking at any studies to prove or disprove this claim, I would have to say that my gut instinct tells me that this could be true. It seems that the people in my parent's and grandparents generations had relatively few allergies and it was to a relatively small amount of possible things. Now it seems much more prevalent.
Americans that eat overly processed foods aren't getting nearly the nutrition they need. Too many artificial chemicals, fillers and preservatives are ruining our bodies and causing numerous food allergies. When the body is constantly allergic to something, the immune system is weakened to where it can't fight off normal diseases such as colds and flu.
No, the amount of preservatives is not what is making people allergic to certain things. There has been food allergies around for a long time, and it is genetic whether or not you are allergic to a certain food. Someone allergic to peanut butter got it from something in their DNA.
The amount of preservatives and chemicals currently used in food processing is not directly related to the recent rise in the number of people experiencing food allergies. This is because people are usually found to be allergic to basic unrefined ingredients as well. Corn, soy, and peanuts organically raised will still cause allergic reactions to sensitive individuals.
The increase in food allergies and food intolerances are actually due to better knowledge and detection of these issues and not because they haven't really been around before. People like to blame preservatives because they believe that they are implicitly harmful - a chemical name has to be bad, right?