There is no Credit/Debit Card on the Apple Online Store associated with your Apple ID
I talked to Apple Support on the phone. They directed me to visit the url:


  https://www.apple.com/shop/browse/account/home


Under "Account Settings", click "Shipping and billing".

This brings you to a much older Apple website, still styled with aqua controls!


  https://secure1.store.apple.com/shop/account/setup_default


I was able to add a new credit card on this site.

When I return to the Developer Program site, the red banner has gone away.