So you can have that right, so long as you don't exercise it.
Gotcha.
The negative prohibitions of the Bill of Rights and the 14th amendment, apply to the actions of government, not private individuals and corporations.
The positive prohibitions that apply to private actors comes in the form of anti-discrimination law, regulations on parking, labor law, employment and public accommodations law, primarily passed by state governments under their plenary police powers.
When did Washington State pass a law requiring no discrimination in public accommodations against lawful gun owners in a similar fashion to other protected choices such as religion and marital status? Oh, that's right, they haven't. We're going to have a difficult enough time just getting parking lot protections. Your right on private property to carry openly, or even at all, or just being on the property, is solely at the whim of two authorities: The property owner, and the government using it's plenary police power with positive prohibitions against owner action against you.
When you sign the Costco membership agreement, there is regulations on your behavior. At this time, there is nothing in the agreement that speaks about firearms. That will change if you and others continue to open carry at Costco. You remember how Peets Coffee and California Pizza Kitchen banned all carry because people kept doing UOC at their California locations? That occurred because the anti-gunner groups successfully pressured them.
Your rights do not exist on private property, unless by their consent or positive prohibitions by a state under their plenary police power.
South Carolina also doesn't have open carry. Perhaps you should fix your own house before scolding people 3000 miles away for having prudence and discretion in open carrying? You have plenty of Sams Clubs in your neck of the woods, but we have maybe two Sams Clubs throughout the entire Seattle Metro area (North Seattle and Tacoma).