Final answer:
Early indigenous churches in the 1930s typically moved towards autonomous church government, reflecting a broader trend towards independence and self-governance in colonized nations during this period. Although these churches sometimes maintained connections to missionary frameworks, they were characterized by leadership that was increasingly African.
Step-by-step explanation:
The early indigenous churches of the 1930s, particularly in Africa, began to develop forms of church government that reflected their desire for autonomy and a denominational structure less tied to missionary influence and more rooted in African leadership. While the specific forms of church government would have varied by location and denomination, it was generally characterized by a move towards self-governance and away from external control by American or European missionaries. This was part of a broader move towards independence and self-determination in many colonized nations during this period. In the wider context, the aspiration for self-governance can be linked to a general global trend towards democracy and away from colonial rule, where indigenous populations sought to establish their systems of governance that were influenced, but not controlled by, their colonial predecessors.
Given the information provided and the broader historical context, option a) Essentially autonomous church government with the American missionary serving as general overseer, is the statement that best describes church government in early indigenous churches of the 1930s. This reflects the movement within these churches towards self-governance while still maintaining some degree of connection to the missionary framework that had initially brought Christianity to these regions.