MP=Marianas Protectorate. The likely alternative abbreviations, NM and MI were already taken. And the Northern Mariana Islands were likely part of the Trust Territory of the Pacific when the postal code was issued, not the commonwealth they are today.
That's not quite the whole story. The original two letter postal abbreviation for the Marianas was CM for Commonwealth of the northern Marianas. (CM is still used by the Coast Guard for boat registrations.) However, then the decision was made for the outlying areas to use the same two letter abbreviations as ISO 3166 country codes. CM was already in use as Cameroon so it had to be changed.