When people boycott a grocery store, or any other store or company, they usually do that for that store or company to change. Since they usually care more about profit than their customers they will not listen to a few people or even a lot of people if they continue to buy products no matter how much they dislike the store.
When you stop buying their products they lose money. When enough people stop buying the products they will be forced to change or stop existing. They can not function without profit and thus have to adapt for that profit to come.
