The Inquisition played an interesting role in the Spanish colony of Nueva Grenada. Slaves found that if they brought themselves before the Inquisition and claimed that they had been beaten until they blasphemed, they might be sold to a kinder master because the Inquisition saw blasphemy as a danger to the slave's soul. If the slave was sold to another owner, the soul of the slave could be more easily saved since they might be beaten less or less viciously. Consequently, slave owners began to resent the Inquisition.

However, the Inquisition was seen as a good thing by slave owners as well. One crime that the Inquisition persecuted in particular was witchcraft. Masters were constantly worried that their slaves were casting spells and cooperating with the devil. Even worse, these practices might create the means to create a slave revolt. The Inquisition was useful to slave owners because it provided a means for them to legally punish their slaves and hopefully suppress a rebellion.

Block, Kristen. Ordinary Lives in the Early Caribbean: Religion, Colonial Competition, and the Politics of Profit. Athens : University of Georgia Press, 2012.

Guengerich, Sara Vicuña. “The Witchcraft Trials of Paula Eguiluz, a Black Woman in Cartagena de Indias 1620-1636.” In Afro-Latino Voices: Narratives from the Early Modern Ibero-Atlantic World, 1550-1812, edited by Kathryn Joy McKnight and Leo J. Garofalo, 175-193. Indianapolis, Indiana: Hackett Publishing Company Inc., 2009.

Landers, Jane. “The African Landscape of 17th Century Cartagena and its Hinterlands.” In The Black Urban Atlantic in the Age of the Slave Trade, edited by Jorge Cañizares-Esguerra, Matt D. Childs and James Sidbury, 147-162. Philadelphia, University of Pennsylvania Press, 2013.

Olsen, Margaret M. Slavery and Salvation in Colonial Cartagena de Indias. Gainsville, FL: University Press of Florida, 2004.

The Spanish Inquisition was seen as disadvantageous to Spanish political interests by the Spanish authority of Louisiana at least as early as 1789, about 300 years after it had been founded and 45 years before it was disbanded.

I'm currently reading a history of New Orleans/Louisiana "The French Quarter" by Herbert Asbury (55-57).

In Spring of 1789 a Capuchin monk by name of Antonio de Sedella arrived in New Orleans on a secret mission to establish the Inquisition there. He informed the Spanish Governor Don Estevan de Miro of his mission and requested the assistance of soldiers. That very night the Governor had the monk arrested and placed on a ship under close guard until it sailed the next day to Cadiz.

Gov. Miro officially explained his actions to the Spanish government in a June 3rd, 1789 dispatch (Asbury quotes the dispatch citing Gayarre's History of Louisiana, Vol III, pg. 270-1). Gov. Miro was ordered to increase the populations of Louisiana and to attract the settlers from the Ohio river network "under the pledge that the new colonists should not be molested in matters of religion, provided there should be no other public mode of worship than the Catholic." Miro further explains that the presence of the Inquisition would go against his objective as it would scare away people.

Perhaps it is best to start answering this question by giving some idea of the actual severity of the inquisition in Spain. In the first 50 years of the inquisition (it began in 1478) conservative estimates suggest that 1500-2000 people were burned at the stake. Between 1540 and 1750 roughly 1000 more people were burned at Spanish autos de fe, during this period far more people were executed in Spain by the traditional justice system than by the inquisition. In a country with a population of 6 million these numbers are significant but they don't really justify the reputation which the Spanish Inquisition has held for the past 400-500 years. The exaggerated severity of the Spanish Inquisition is often referred to as the 'Black Legend' by historians and seems to have been caused by what was essentially protestant propaganda.

The author who holds the most responsibility for this 'black legend' is probably Reginaldo Gonzales de Montes who published A discovery & playne declaration of sundry subtill practices of the Holy Inquisition of Spayne in 1567. It was very widely read and printed for English, French, Dutch and German audiences before the end of the decade. After Reginaldo's success the legend was perpetuated by more protestant authors in the 17th and 18th centuries, notably James Salgado's The Slaughter House, or a brief description of the Spanish Inquisition in 1687 and John Marchant's Bloody Tribunal in 1756. Outside of Spain the inquisition had certainly gained its a reputation as a bad thing while it was occurring, from the mid-late sixteenth century onwards. Within Spain, and even within the rest of the Catholic world it did not have had the same kind of negative reputation, this isn't to say Catholics liked the inquisition they just had a more realistic idea of how bad it was.

This is a good question, as it actually plays into a novel I'm working on (about the rise of the Spanish Inquisition, the Fall of Al-Andalus, and the consolidation of Spain). In my research, I've found that there are instances of people hating the Inquisition from the very beginning (at least of the Inquisition as we think it), although these tended to be more for political reasons than for moral. In the beginning, Ferdinand and Isabella were reluctant to begin such an institution because it made the church more involved in secular affairs, and only agreed once they became convinced that conversos would fuel further civil wars in Iberia (it is at this point that I should note that Ferdinand and Isabella's power was weak at this point, and they only just got out of a civil war involving Isabella's sister).

Once the ball got rolling, the Pope condemned the Inquisition in the early 1480s, seeing it as a fire that spun out of control. I haven't gone into too much research behind the Pope's reasoning, but my guess would be that by this point, the Inquisition was a state institution which gave Ferdinand and Isabella power, and not the church.

By 1485, we even see Spaniards turning against the Inquisition. Notably, the people of Seville refused to let Inquisitors inside the city, although the reasons for this were more because they saw the Inquisition as an Aragonese power infringing into Castille.

Chris Lowney's A Vanished World provides a good but brief description of the early Spanish Inquisition.