Alice in Wonderland.
Most islanders believe in a kindly God, the Way of the Goddess, and in a benevolent Universe. They feel they are meant to be here and they do their best to care for one another. Since the first settlers were overwhelmingly women (and charismatic, adventurous and a bit scurrilous) a matriarchal society, complete with Goddess-oriented religious practices became the status quo.
Of course without the help of the Russian Empire beginning in 1821, these early New Islanders would have remained an extremely primitive nation of impoverished Gaelic farmers. Though Russia extracted great quantities of whales, seals, fish, timber, and the local (sacred) otters, their presence was an unintended benefit. The Russians only wanted to extract raw materials, then later to secure an outpost from which to watch (and pester) the Americans and Australians. They did all this with almost no contact with the islanders other than to demand farm-produce quotas from them, but usually with an offered carrot in return.
This they accomplished by importing supplies like cookware, nails, seeds, tools, cloth, and some goodies like chocolate, coffee, tea and vodka. Beginning in the early 20th Century, the Soviet Navy and later the KGB enjoyed huge budgets with which they built concrete roads, hydroelectric dams, streets, railways, medical centers and other infrastructure to modernize the island.
In the Russian commanders' eyes, the islanders tended to be a bit spacey, and therefore unpredictable (and potentially dangerous) but yet proved themselves to be willing to fulfill the quotas and were a fierce guerrilla force in defending the island's coasts. So the standard procedure was to let them alone: islanders ran their own towns, schools, cultural affairs, police and governing. In 1992, the Russians graciously left all the infrastructure intact, except the airport control tower and military installations.
Next: more on New Island's culture