I use cloth bags, too. But, ignoring the marine dumping problem, cloth bags can be the worst.[1] You would need to reuse each thousands of times to be worth using over LDPE bags.
That's more an indictment of cotton than reusable bags. Other materials are fine.
Even better are foldable bins made of cloth—I think mine are reinforced with cardboard or semi-hard plastic inside. They stay open when loading with groceries, and don't roll around in the trunk of the car.