"Tartan" is Scottish for "plaid". Tartan fabric is almost always 100% wool, and there's nothing "official" about it. "Jewish Tartan" doesn't mean "Tartan for Jews" any more than "Kentucky Fried Chicken" means "Chicken for Kentucks". My kilt is a McDonald of Sleat (http://www.scotsconnection.com/uploads/images_products/557.jpg) tartan. I happen to have McDonald blood, but the colour of your tartan usually has more to do with what colours you like and what towns you've bought tartans in than who your family is.
Warning: Pedantry Alert