If my capital one card is stolen? Odds are, capital one will cancel and re-issue the card before I even notice. Otherwise, I notice it when I skim my transactions while paying my bill. And with a credit card? Absolute worse case scenario, I have a lower limit for a few days while they resolve the fraud. More often they just instantly pretend it never happened and deal with it themselves.
Contrast that with debit cards where you potentially have the equivalent of a hold on your bank account.
I have zero concerns over having my credit card stored in firefox because it really barely affects me if it is stolen. Which is the way to go.