Short answer to the questions: No. Yes.
Answer with reasoning:
Stores are private property and staff generally have the right to refuse entry, or to require someone to leave. Entry onto private property is done under a form of legal licence. It assumes you're there for a legitimate purpose and with the consent of the property holder (i.e. owner, tenant, business). That licence can be subject to requirements. While this licence is not a contract, it can be helpful to think of it in a contractual manner. Effectively: The business is agreeing to allow you to enter their shop subject to you agreeing to the conditions of entry.
In terms of bag searches, the entry condition is that you agree to allow the business staff to inspect the contents of your bag should you be requested to do so. For that to be a valid condition, the store needs to tell you about it being a condition before you enter. That's why to allow bag checks, the business must display prominent signs at all entries which state along the lines of it being a condition of entry.
If you subsequently refuse to allow a bag check if called on to do so, you've breached a condition of entry to the store. The business is then within their rights to refuse you further entry to their store, which is private property. In effect, the licence extended to the general public is revoked in your specific instance.
It's not extortion or blackmail. It's a denial of entry in circumstances where they are well within their rights to do so.