Every day we are all exposed to some level of chemical fumes. When you get in a new car, the "new car smell" is largely caused by chemicals given off by new plastics. Spray paints and household cleaners give off fumes. Different plastics and wood products in your home give off odors from adhesives and finishes, especially when new. But normally these fumes are at such a low level that they cause no problems.
If you look at the comments for the article How Icynene foam insulation works, however, you will see a number of people who have become sensitized or allergic to the fumes given off from icynene insulation. What seems to happen is that these people enter the home shortly after the foam is applied (or during application), while it is still curing and giving off a lot of fumes. Their bodies get overexposed to the vapors and become sensitized. From that point on, any exposure to even a minute amount of the chemical causes a reaction. The process of sensitization can make a home unlivable for people who become sensitized.
This sounds odd, possibly impossible, until you start researching the process of sensitization. This video offers a quick look at the problem in the automotive paint industry, starting at 2:05:
With today's hardeners and clear coats, I've heard of people getting sensitized from a single over-exposure and having to leave the industry because of severe allergenic reactions from even the slightest contact with fumes. I personally know of people who can't be in the same room as fresh clear coat or overspray. So that to me says that the warning labels have to be taken seriously.
This page offers a similar perspective:
Sensitization, in this case, is the state of being allergic to epoxy. Sensitization can occur at any point, regardless of how many times or for how long you've been exposed to epoxy. Your chances of being sensitized will increase if you're exposed to a greater amount of fumes in an unventilated area, but even one episode of exposure can lead to an allergic reaction. This is why preventative safety is so important in regard to epoxy. Once sensitized, even small amounts of the substance can trigger allergic reactions and it will be increasingly difficult to work with the material. There is also no definite cure for sensitization, only methods to relieve the symptoms.
This article from the Mayo Clinic on occupational asthama explains how the process begins:
Asthma can occur when the body develops an allergy from continued exposure to a substance. Your body starts to identify the substance as a threat and activates your immune system to react. This is called sensitization. You don't have symptoms at first because the sensitization process can take months or even years to occur. Symptoms start when your immune system begins to produce specific antibodies against the irritating substance. This, in turn, triggers the release of chemicals, such as histamine, which inflame the lungs and cause asthma symptoms.
That article mentions longer time spans. When fumes are heavy, however - for example in a room filled with paint fumes or an unventilated house filled with fumes from curing insulation - sensitization can occur in hours. And then, once you are sensitized, even mild exposure causes a reaction.
This page contains the following cautionary quote about spray-on insulation:
Spray polyurethane foam (SPF) insulation is a highly effective weatherization product that is playing an important role in national efforts to dramatically increase the energy efficiency of our homes, schools, and buildings. However, SPF foam contains diisocyanates, and dermal or inhalation exposure to these chemicals can cause significant health risks, such as asthma and lung damage, if specific workplace precautions are not followed during product application and clean-up. Risks also may apply to building occupants who may remain on-site during or re-enter shortly after application.
What can you take away from this? Clearly, you do not want to become sensitized. When any outgassing chemical is being applied or is drying/curing - paints, foams, fiberglass, whatever - a high-quality, appropriately rated respirator is mandatory. These respirators are not that expensive - $30 at Home Depot will buy you a good one. If you are having foam sprayed in an existing home, you want you home to be maximally ventilated so the fumes do not get into clothing, furniture and carpets, and you want to stay completely out of the home during the entire curing cycle. If you must enter the home, wear a respirator like the workers do.
Read the comments in How Icynene foam insulation works. Sensitization does not apply to everyone, but it does apply to many. Take appropriate precautions to avoid becoming sensitized yourself.
See also: How Allergies Work and asthama