Dave Ramsey would tell you that debit cards from MasterCard and Visa offer the same $0 fraud liability protection that credit cards do.
From his website:
What most people don’t realize is that credit companies like Visa or Mastercard protect their debit card purchases too. If you run your debit card as credit when you make a purchase (which may show up as “pending” on your account), you have the exact same protections as a credit card.
He's not wrong in saying this. When you use a MasterCard or Visa (as well as other card brands), you have $0 fraud liability, whether that card is a credit card or a debit card. If a fraudulent transaction comes through, you dispute the transaction, and the bank will give you your money back. A thief using your card in this way has ultimately stolen from the bank, not from you.
However, there is a difference between how credit cards and debit cards work. When a charge is made on a credit card, the amount is borrowed/applied to your credit limit. If a fraudulent charge comes through, it is not a big deal: you dispute the charge, the bank investigates and removes it, and you never have to pay it.
With a debit card, though, charges are removed from your checking account immediately. As a result, a large fraudulent charge can potentially empty your bank account before you realize what has happened, which can result in further problems when you make legitimate purchases. In the end, the charge will be removed (the charge can still be disputed and the bank will give you the money back), but in the mean time if your bank account is empty you will have legitimate bills that need to be paid, possibly incurring overdraft fees or late penalties.
If you want to get rid of credit cards and only use debit cards, there are ways to mitigate the risk. If you keep a fairly large balance in your checking account (you can do this by keeping some or all of your emergency fund in your checking account), then a fraudulent charge is less likely to remove most or all of your balance. Another way to handle the risk is to purchase identity theft insurance (which Dave Ramsey recommends) that can work with the bank to solve the problem and pay for any losses you incur as a result.
Personally, I would describe myself a a fan of Dave Ramsey and have benefited from much of his teaching. However, I do use credit cards on a regular basis, because I see debit cards as too much of a risk for me. I use the credit cards as if they were debit cards: I only purchase things using my credit card that I already have the money for, and when a purchase is made I account for that purchase right away in my budgeting software even before the credit card bill is ultimately due, ensuring that I have the money to pay it in full each month. However, for some people that I know, the temptation for using a credit card irresponsibly is too much, and they are better off not having a credit card.