... Radioactive fallout \'dust\' is dangerous because it is emitting penetrating radiation energy (similar to x-ray\'s). This radiation (not the fallout dust) can go right through walls, roofs and protective clothing. Even if you manage not to inhale or ingest the dust, and keep it off your skin, hair, and clothes, and even if none gets inside your house, the radiation penetrating your home is still extremely dangerous, and can injure or kill you inside.
So how they think a few thin sheets of plastic will save them inside the house... What stops radiation is simply putting mass between them and the radiation source. Like police body armor stopping bullets, mass stops (absorbs) radiation. The thicker the mass, the more radiation it stops.