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.
A true lover of nature does not despair now that his mistress has turned a colder cheek.