Question

How did the identities of colonizing and indigenous American societies change as a result of contact in the Americas?

Answer 1

The colonizer's identities did not really change. The indigenous societies suffered from forced change that often eradicated major parts of their cultures.

Explanation:

The mindset and expectations of colonists were not really changed by indigenous societies in the Americas. They came as 'conquerors' to establish extensions of their own cultures in a new place, and they did.
It was the indigenous cultures that always were changed forcefully by either direct action of the colonizers or as a defensive action to mitigate the impact of the colonists on the indigenous people.
In most cases "acceptance" in the new order required indigenous people to abandon their own cultural identity to take on the 'identity' of the colonists' culture.

The following is an excellent discussion on why colonizations did NOT produce the same effects worldwide.
http://mufwene.uchicago.edu/classes/Cultural%20Consequences%20of%20Colonization.pdf