Ramsey doesn't mandate cash, they are fine with debit cards which have the convenience of online shopping. There are two separate issues, one is the very usage of debt, the other is the amount spent because of it. Whether or not they are connected is debatable but they don't push the point so much on the pod.
I actually like the DR pod for the way they give over their message, they spend most of the time discussing ways to be proactive, to be intentional with money. If you are truly intentional you won't spend more, be it cash debit or credit, and if you are not intentional using cash is just a hindrance, not a mentality shift. They only recommend cash when someone has unchecked spending habits.