Wouldn't it be better to solve the root cause instead of the symptoms?
Give residents a legal right to open a bank account - as it's for example the case in some European countries (e.g., in Austria banks are required by law to provide at least a "basic" bank account to people that don't have any other bank account at another bank).
With this approach the stores would still be inaccessible to unbanked people - but everyone would have the choice to become "banked", even if they have a bad credit history, etc.