... a shoplifter. It can't be used to justify a routine check.

Membership clubs like Costco and Sam's Club have explicit requirements in their terms of membership that you are required to submit to a review. Here are the relevant sections from Costco's terms and conditions that I just copied from the app:

-Costco reserves the right to inspect any container, backpack, briefcase, or other bag, upon entering or leaving the warehouse and to refuse entry to anyone at our discretion.

-To ensure that all members are correctly charged for the merchandise purchased, all receipts and merchandise will be inspected as you leave the warehouse.

If you don't comply, they can revoke your membership, though it would probably take a bit of work on their end to figure out who you are.

At a random store like Walmart, they don't have a right to stop you and review your stuff unless they suspect you of shoplifting, which would then fall under shopkeeper privilege. Depending on the state, there may be additional rights they have at that point, like the ability to detain you until police arrive. But absent some sort of suspicion, there's really nothing that a regular store can legally do.