In some houses even solid wood can be eliminated. The best reason to eliminate all forms of wood is to eliminate the need for toxic termite treatments. Combustion appliances include gas water heaters and ranges, oil furnaces, wood stoves, etc. If it has a flame, it doesn't belong indoors. The high efficiency models with closed combustion chambers are, of course, less polluting, but they are still a compromise.
Gas ranges and unvented kerosene space heaters are by far the worst offenders.
Most range hoods are not nearly powerful enough to adequately remove the combustion gases that build up in the kitchen and the only way to dilute the fumes of a kerosene space heater is to throw open the windows. An extra powerful range hood and open windows certainly do not contribute to energy efficiency and they won't necessarily make the appliances tolerable. After eliminating the big three, the materials used inside the house, within the living space, are more important to consider than the materials outside the house. While metal roofing is less polluting than asphalt containing shingles, it will not be as critical as selecting a tolerable interior paint. Of course, if your sensitivities are severe, every component of the house should be selected with care.