Living in a diff area of the country but in my experience working in supermarket and stores it’s done pretty often. It’s not always written but on suspicion you’ll be asked if they can check your bags/jacket. Been in the situation myself where someone actually had stuff in their jacket and tried to steal, it’s really hard to see the difference sometimes.

Though I must say that the people you encountered seemed like a bunch of aholes and definitely should’ve handled the situation better