The way I do it is my salary goes to a online savings account (~2% interest) that's not linked to any cards. I have a debit card I move money over to when I need cash out or to use it (simple with the bank's app). Then I have a CC (used for utilities etc) which I pay every billing period from the savings account.
Works well.
So worst case you are without a small amount of money during any dispute/fraud resolution period, but your major regular ACH payments are not at risk.
The downside is having to monitor your balances closely and transfer funds more often (which can sometimes involve a fee but if you shop around you can find banks that don't change a fee for inter-account transfers).