A group of people within the domain of a state creates their own organization in an effort to challenge inequities and assert their political rights to resources and recognition within their state. What is this type of formal organization called?

Civil society organization is the correct answer.

Civil society organization (CSO), also known as non-governmental organization, is a group of people within society that unite with the primary purpose of asserting their political rights and seeking recognition within the state by challenging inequities regarding human rights, environment, anti-corruption and labor standards.