These make more sense than many of the reusable bags currently on the market: I hate the idea of carrying meat in a bag that can't be washed. What I don't like about those and many cloth grocery bas is that there's no structure, so things are likely to get squashed by the pressure of the sides.
I have a couple reusable bags I got at Fresh Farms that I like: they're made of some kind of plastic-coated canvas (kind of like duct tape, but not sticky or stretchy) and are sewed into the same shape as an old-fashioned paper bag, although they're a bit bigger. They're very sturdy (right now one is holding most of a bushel of apples,) and while they aren't machine washable, they're easy to wipe down.