I shop at Costco and Sams and do not have to show an ID to get in. Just one of their issued cards.
And I’ve never had to show ID when leaving Costco. I never have to show ID when using credit or debit cards either. I just swipe, tap or insert my card. The checker never even touches it, let alone asks to see some ID.
In CA their cards have a picture on it that the check with your face.