It's Okracoke, NC. The Okracoke Brogue (1997, 20 minutes):

https://www.youtube.com/watch?v=8Uuzr_gl4Oo

From the mountains to the sea, NC has quite a range of accents ("Voices of NC"):

https://www.youtube.com/watch?v=dAGG3LnEVvI

Previously the BBC covered Tangier, VA with nearly the same headline ("The tiny US island with a British accent"):

https://www.bbc.com/travel/article/20180206-the-tiny-us-isla...

Short documentary on Tangier Island:

https://www.youtube.com/watch?v=upKqzxuJ5L4

Newscast from the 1970s about Tangier:

https://www.youtube.com/watch?v=96sHf5YDZj4