Styrofoam is a registered product of Dow. The packaging council has an explanatory page at http://www.polystyrene.org/facts.html
The styrene product is a neutral product used almost everywhere, so when you go to get convenience food, it is the cup and container that you take it home in.
If mold is a problem, that needs to be solved, the mold can build up anywhere there is moisture and little sunlight.
If you worry about styrofoam, don't use it in the house, you don't have to. The foil-faced insulation used on the exterior is not styrofoam, but polyurethane or polyisocyanurate. Unlike styrofoam bead-board, which allows air, dirt and moisture to get between the beads - these products are closed-cell foam covered with aluminum foil to prevent the problem.