The business has the right to choose if someone is allowed to carry on their private property. They are also obligated to post signs and if any employee asks the person to leave, then I would leave even if it isn’t clear... unless you knew the company policy to the letter.
Does a business have the right to allow smoking in their restaurant. I mean it is private property right? Rights are given by God and defended by the Constitution. Or they used to be. Now it appears they are defended by the barrel of a gun.