Also you can have cashless payments why still supporting cash. They aren't mutually exclusive

Yes, but "cashless society" means one devoid of cash payments. Some countries are talking about getting rid of cash entirely. Cash payments and digital payments both being used in concert is what we have now, there would be no need to "transition to a cashless society" from that to that again, the difference is they want to end cash, entirely, all of it, gone, only digital payments. Thus making "cash" and "cashless society" quite mutually exclusive, actually.