If the logic here is that dollar stores are somehow unfair competition for local grocers because they are cheaper or that they don't sell fresh food or whatever, then....
We should be "targeting" CVS and Walgreens as well. Those two have become two of America's largest sellers of groceries for some of the same reasons that dollar stores are popular: lots of locations, easy parking or walkability in urban areas, convenience of being able to get more than just groceries. And dollar stores have the advantage over the drug stores of having low prices.
How exactly is this bad for low-income folks? And why are activists targeting firms that are willing to locate in neighborhoods that others aren't? Why go after the firms that improve the lives of poor folks (the dollar stores) and not the ones used by middle-class parents in a hurry and willing to pay higher prices (the drug stores)? Is this not pure progressive paternalism and classism?
Is this just a pure "localist" argument? If so, recall these words of wisdom from an economic historian friend: "We tried localism. It was called the Middle Ages. It didn't work out so well."