Yes, they can refuse certain kinds because it's not a debt. You load groceries onto a belt and walk away, it's not a debt at that point. You stay at a hotel, this incurs a debt if you pay after the stay. If they accept cash, they have to accept any cash. They don't have to accept cash at all, which is what this place does. The cash is simply an accepted, backed means of conveyance with a standardized value. Hotels usually require a card up front regardless for which they will tell you is for charges, so the point is moot. If they hadn't clearly posted that they didn't accept cash, they'd have a hard time refusing it.