To what extent did the American Revolution fundamentally change American society?
Very little actually.
Long before the American revolution, America had been acting very my like an independent country. Of particular note was our relationship with France which from the beginning was very good. Conversely, England's relationship was with France during the same time was at best stormy and at worst, warring.
The greatest change realized by Americans was the form of government they enjoyed. But the impact was negligible because the basic government of each of the 13 states did not change after the Revolution from what is was before.
Americans still had to pay taxes only they no longer went to England. They still had to raise a military, provide basic human services, build roads and join in commercial ventures.
The most telling change was the lack of British influence in their everyday lives. But most of the laws were the same, the basics of society were the same, and their local economics remained unchanged.