Some stores have a policy that you can't have a backpack or can't have a bag over X size. They typically say you need to leave your bag unattended at the front of the store.
This is common in areas with high rates of poverty, theft and homelessness. It's intended to reduce theft.
In reality, it is an anti-homeless policy which punishes an entire demographic for the bad acts of a few and someday someone way well get sued over this fact. (They can't do this based on skin color, gender, etc. They shouldn't do it based on "very poor, too poor to have housing and/or a car,".either.)
I read a post on r/homeless by a guy who had more than a thousand dollars of prescription medication in his bag AND other people were not being instructed to leave their bag unattended because they were not obviously homeless.
Lots of homeless people have health issues and that bag may contain everything they own. If it disappears, it's potentially a life-threatening disaster for that individual.
Most homeless are on the street alone and have no one they trust to watch their bag. It's rare to have adequate access to storage, something I've written about before.
Stores that want to exclude your bag should provide lockers to lock it up. This would also help people who live without a car to run multiple errands because they could lock up stuff they bough elsewhere and get that one last item on their list or whatever.
Small stores, like Family Dollar, could have two to four lockers. Large stores, like Walmart, could readily have 6 to 9 lockers in their spacious foyer areas. (They could also be more consistent about providing benches in that area.)
Off the top of my head:
The greeter at Walmart or cashier at other places could have the key to the lockers and give our a numbered token of some sort to let you reclaim your bag(s).
Various places could come up with various procedures, depending on exact details for their store and other factors. This is a place to start, not a comprehensive answer.
No, I don't think this is an argument for allowing homeless people to bring a giant cart of stuff into the store. I think you can place limits, but this limit is de facto an anti-homeless policy and is handled in a highly problematic fashion and doesn't have to be.
People routinely bring purses and other bags into stores. If you said "No purses!", some women's lib organization would be dragging you into court by the end of the week.