This is exactly why I have Visa, Mastercard and Amex cards.It doesn't guarantee you won't get buggered, but it does make it less likely.
That helps a bit. But if the company you want to use your Mastercard/Amex with has Visa as its merchant services provider, they still can't accept any card payments, no matter which company name is on the card. As anybody in certain shops will have seen in the chaotic scenes yesterday afternoon, although those of us who moved quickly were able to clean out the nearest cash machines.
People complain about ramshackle banking systems and there's a lot of truth there; But worth thinking that if the industry were redesigned from the ground up, they'd probably have a single payments processor, and that would act as the processor for cash machines as well. In that instance a system failure would have left people with no cards and no cash machines.