“Or was he born in Hawaii and became a US Citizen when they became a state?”
When Hussein was born (even if he was born in HI — which he wasn’t), HI was a state.
But if HI still was a U.S. Territory, wouldn’t someone born there be a U.S. Citizen? (I don’t know.)
Hawaii was an incorporated territory from annexation. Any person born in the Territory of Hawaii after August 12th 1898 was a natural born American citizen. Both Alaska and Hawaii were considered integral parts of the United States, not possessions as defined by the Insular cases.
The same applies to Alaska, anyone born in the Department, District, or Territory of Alaska after October 18, 1867, was a natural born American citizen.
The Insular cases in the early twentieth century drew an (unconstitutional) distinction between incorporated territories (Hawaii, Alaska, Arizona, New Mexico, Oklahoma, and the Indian Territory) and unincorporated territories (The Philippines, Puerto Rico, Guam, American Samoa).
However, the Congress has partially fixed this with acts guaranteeing citizenship in all territories except the Philippines (now independent) and American Samoa (due to local issues of governance and land ownership).
Even under the insular cases, both the Virgin Islands (1917) and The Northern Mariana Islands (1986) have had citizenship since acquisition.
Goldwater was born in Arizona when it was a territory before it became state.