Our new software for mailing statements and assessing postal rates will kick out statements that have an address different than the US Postal Office (usually because we have a Rural Route addres on file and the USPO has a street address due to changes for 911 emergencies). Can we update the addresses on our system to match the ones the USPO has without notifying the customers?

I'd be very careful about this. As a customer, I would want my statement mailed to where I told my bank to mail it: the address I provided. And how can you be sure that what the post office has is more current than what you have? I'm thinking a messy divorce situation where the wife wants her statement sent to a rural route address she just gave you yesterday but the post office kicks out her old street address where her soon-to-be-ex-husband lives kind of thing could get you into hot water by causing you to send her statement somewhere she doesn't want it going.

At my FI, we don't change addresses for any reason without a customer signature authorizing the change. It avoids any uncertainty.

I agree. We require a customer's signature to change any address. It is a Red Flag & could cause identity theft if the info ended up in someone else's hands