Plum Creek Mercantile makes their bags from 100% cotton twill. There is no plastic lining. You can use them for almost any foods besides liquids and soft fruits. Just machine wash or handwash. These snack bags come in different fabrics (the robots are our favorite) and sizes and have a velcro closure.
This could also make a fairly simple DIY project. Let us know in the comments section if you have made anything like this yourself.