For something small or temporary, I might overlook it. For something that has direct access to my bank account, no go. They need to accept some liability if they want that level of access to my financial life.
To be fair, Paypal has an arbitration agreement too. But, if you're using Paypal as justification for your own policies, that's not exactly a strong starting position.
Have a look at Revolut (however, you need a monthly subscription to use disposable virtual cards).
I also social engineered my way in to my own account via a brand new Twitter account, so ... beware.