What a curiosity. It appears that other territories count by statute but for American Samoa the US national designation was created to give them similar rights to citizens but not voting or political office and in exchange the Samoans get some more self-determination than other territories. Cool!
Yes, lots of them don't want the 14th amendment. They have racist/ethnocentric land ownership laws that contradict the 14th amendment, the same one that creates birthright citizenship.
There are also allegedly some low quasi-government tribal positions in remote areas where women are effectively ineligible for office, though this one is less provable, it also would not be consistent with constitutional protections.