Final answer:
True, the Spanish sought to control Native Americans by imposing labor systems and converting them to Catholicism, but native resistance led to periodic autonomy such as during the Pueblo Revolt of 1680.
Step-by-step explanation:
The statement that the Spanish wanted to establish strict control over the Native Americans through intense labor and by converting them to the Spanish Religion is True. The Spanish conquest involved both conversion to Catholicism and the exploitation of native labor through systems like the encomienda and repartimiento.
Missionaries, while aiming to convert the native peoples, sometimes grew to understand and advocate for the rights of the natives. Despite some attempts to integrate Christian practices, Native Americans often resisted, leading to events such as the Pueblo Revolt of 1680 that briefly restored their autonomy.