Paper bags are better than plastic, but with the ban on plastic bags, a simple solution is to do what I did.
I harvested a tree from my property in Brinnon, milled it and built a box with compartments to put in the back of my truck when I go to get groceries, etc.
Simply put your purchased items into the sustainably harvested wooden box in the back of your truck and haul them home.
You will have to yard that shopping cart across the parking lot to your truck, but you would do that anyway.
If you are unable to harvest a tree, call a logger.