No, passwords, SSNs, PINs and Credit Card numbers should be hashed before inserting into any table. There is NO reason for anyone to save that data unhashed.
To compare data, just hash what the customer enters and compare the hashes. Why is this so hard for 99.9% of companies to understand?
ACH processing requires sending bank account information to the ACH along with how much to bill the individual. Many other forms of automated payment processing formats also require credit card numbers sent - this is all happening with flat files. If you expect credit card numbers to be hashed in your database, then you need to convince the receiving end of that data that they do not need the source to send that data.