The one by me in Maryland does the same thing if you have an item that’s not in a bag.
If I’m going to go through the trouble of stealing something, it’s not going to be a case of Mountain Dew.
I walk right past them and wish them a nice day. The 4th Amendment makes what they are doing illegal.
They are demanding to search my property. The moment money changed hands at the register, the items became legally my property and they have no right to make me prove it.
The onus is on them to prove that it is not my property and under the 5th Amendment, I don’t have to self-incriminate.
The 4th and 5th Amendments have nothing to do with whether or not the store can stop you. Any rights there are based on state or local law.