sondra, there are many different types of plastics and other synthetic materials that are quite safe to cook with nowadays. my wife just bought me 2 pot holders that appear to be rubber, but are made of a high temp synthetic, so they won't melt. it took me a while to get used to grabbing something hot with a rubbery little mat, thinking it would melt to the handle.
i'm sure the plastic in the steamer is suited for cooking temperatures.
The way that you wander is the way that you choose. The day that you tarry is the day that you lose.
Sunshine or thunder, a man will always wonder where the fair wind blows.