Keeping in mind that keeping the oceans clean, is definitely a good thing, and you can feel good about not using plastic bags, when you have replaced them with reusable (fabric) grocery bags, for the sake of "going green" -- the tips at How to Keep Reusable Grocery Bags Clean and Safe - Wash Your Reusable Grocery Bags for Safety are quite resourceful and informative.
Remember: The fact that, not only is keeping the oceans clean a good practice; the practice of (also) laundering reusable grocery bags, is a definite plus...