I’m not sure what you’re talking about. A Costco membership is $60 and you can pay in cash. There’s no credit card needed. You don’t have to sign up for their credit card either, and it’s not really even pushed when you sign up for membership. What gave you the impression that you have to qualify for a credit card to shop there?
Until 2016, Costco and Amex had an exclusive partnership. You could pay either in cash or with Amex, usually the Costco Amex tied to your membership card.
Now they take any Visa card, and have converted Costco Amex cards to Costco Citi VISA cards.
Before they accepted American Express they only accepted debit and cash. I remember having the American Express card and being excited that I could finally get cash back on Costco purchases and have a credit card vaguely backed by a company I trust.