More Eternity Shawl
I've discovered the maker of Mary-Kate's Eternity Shawl. It is a designer (with a very cute website) called Suzanne Juul, and there in her Spring 2006 collection is what looks very much to me like a cotton version! (see the right-hand-side of the image)
It does seem however (if you look closely) that her original mohair ones do have a seam, so perhaps it is as simple as knitting a scarf and joining the ends? I wonder though if knitting on a circular needle would work better, or whether you wouldn't be able to knit one long enough. It would be good to find a way of making one without a seam (not least because this would make the name more appropriate)!