I think what Vern is trying to say is that the strapping is made out of a type of fabric, which cloth is considered by many as another term for fabric. I agree, i think the tour suit is entirely made out of a specialized material that feels a lot like rubber.
As for the straps on the original ROTJ suits being made out of ABS, i dont think so. If you pay close attention to the movie,there much more flexible then standard ABS.