We live in a rural state where not every town has a post office. In these cases, delivery of this town's mail may be split up amongst several different post offices. To avoid confusion with street names that may be located in both communities, the towns without their own post office have been advised for mailing purposes to use their OWN town name and the postal zip code for the OTHER town that delivers their mail.

When sending new debit cards, our processor, 5/3, uses an automatic matching feature where it checks to make sure the zip code matches the town entered. If it doesn't, the town name is automatically changed to match the zip code.
This causes a problem and the mail gets returned or lost.
5/3 says they can not turn this off.
Has anyone else ever had this problem?

There are a lot of zip codes for which there is a primary city or town name plus a number of alternatives. That can be true when there has been post office consolidation or when there are branch post offices in outlying villages. It can also happen when the post office sets up arrangements such as you've described. Sometimes the correct delivery address can be determined from the ZIP+4 code.

If you have problems, you could suggest that the vendor deliver all cards to the bank, and you could re-address them (do I hear a groan out there?) Or you can keep pounding on the vendor to stop using the auto-correction feature until the message gets them to change.