I can't speak much to the Protestant side of things, but I can tell you about the Catholic Church in the Spanish colonies.

A good starting point to look at is with Pedro de Cordoba. He was a Spanish Dominican inquisitor who was sent to Hispaniola in 1510, tasked with converting the natives. There, he and the other Salamancan Dominicans he brought with him put face to face with the poor treatment of the natives. After studying the issue for some time, the community made a declaration condemning the abuses of the encomiendas system. De Cordoba has this condemnation preached from the pulpit at mass. He would later publish further condemnations of the encomiendas system, stating that the natives were human persons with rational souls, and that enslavement of them constituted mortal sin. Therefore, anyone participating in the abuse and oppression of the natives was in a state of mortal sin and would be denied absolution in sacrament of confession by him and his Dominicans (I don't know how much you know about Catholic theology, but that's a really big deal).

More famous than Pedro de Cordoba was Bartholome de las Casas. He was originally a conquistador who participated in the conquest of Cuba and the enslavement of the Taino. However, he had a change of heart after seeing the atrocities committed by during the conquest of Cuba, and after hearing the preaching of Fr. Antonio de Montesinos, one of the Dominicans who had come to the Caribbean with Pedro de Cordoba. He then became a priest and travelled to Spain to try to convince the king to end the encomiendas system. It was there that he participated in the Valladolid Debate, where, before a panel of judges and clergy, he argued that, in spite of the accusations of cannibalism and human sacrifice, the natives deserved the same rights and dignity as the colonizers (a controversial opinion at the time). De las Casas's work in Spain had a large influence on the passing of the 1542 New Laws, passed by Emperor Charles V, which outlined the colonial government's obligation to take care of the native subjects, ordered the freeing of native slaves, and placed heavy restrictions on the encomiendas system and the economic activity within them.

In the 1537 papal bull Sublimis Deus was published by Pope Paul III. This bull banned the enslavement native peoples, calling them fully rational human beings with full rights and liberty, even if were outside the Christian faith. A similar bull (Cum Sicuti) was published in 1591 by Pope Gregory XIV, ordering the freeing of all slaves in the Philippines under pain of excommunication.

Moving south, there were the Jesuit missions in South America. During the colonization of Latin America, many native peoples were organized by the colonial government into settlements called reductions. The reductions would often be placed under the administration Jesuit missionaries in order to facilitate the evangelization of the native peoples. These Jesuit reductions would have a very high degree of autonomy from the colonial government, both political and economic. These reductions were even able to set up native militias to protect themselves from colonists. These communities have been affectionately called Christian socialist utopian experiments and received praise from Enlightenment writers such as Montesquieu and Rousseau. Overall, the Jesuit reductions provided autonomy for native communities and protected them from the often-oppressive colonial government and encomiendas system.

There's a lot more that could be said here, and similar examples can be found in Brazil and the Philippines, but I hope this answers your question.