Can banks charge non-customers fees for redeeming savings bonds or credit card cash advances?

I don't believe the bank's contract with VISA/Mastercard would allow charging for cash advances.

Government Savings Bonds, definately not moral to do so. The bank is paid a fee by the government to transact Bonds. They may be in violation with their agreement with the Treasury by refusing to negoiate a Bond for a non customer.

(In fact I'll bet most of the operations people are not even aware the bank is paid this fee, or that there is even an agreement they are supposed to abide by.)

Never mind the morality of charging a fee for cashing bonds. It's prohibited by regulation. See 31 CFR 321.23(b): Charges to presenters. A paying agent shall not make any charge whatever to persons entitled to request payment of securities, for redeeming them under the provisions of this part.