When banks merge or a bank is acquired, a process must be done to map the other bank's products into what our bank has. Is there any regulatory reason why we couldn't map a customer that had an interest bearing account at the other bank into a non-interest bearing account?

Take the regulatory issue out of it, are you wanting these customers to leave? Get ready for some upset customers when they find out, they are no longer in an interest bearing account.

Is there are regulatory issue?

You would have to send 30-day notice to state that the account they are in is no longer being offered and they will be converted into a new type (be sure to include the new TISA disclosure). If you are sun-setting that product type, you convert customers into a different type... I am not aware of any requirement to convert them from a NOW into a NOW.

However, if there is an interest bearing account that is similar to what they currently have, I would HIGHLY recommend you convert them into that. Otherwise, as osucpa said, you're going to have some hella peeved customers.