Well, since we were talking about shopping baskets specifically and not baskets in general I was referring to the former. Those tend to mainly be plastic and on rare occasions metal. If you want to get into what baskets are made of in general they can be made of pretty much anything you can think of. Vines, wicker, branches, rope, steel cables, human hair, tendons, used condoms, etc etc.
Also, a shopping basket is hand held and usually has two handles that fold down out of the way. If you want to be an anus you could call the part of the cart that holds everything a basket but the entire thing is a cart. Of course different areas call them different things but people like being wrong.