Although people have always thought Europeans are the better people and see Europe as superior civilization, people weren't generally racist back in 17th-18th century.
We have de Gerando for example who said, "human nature was fundamentally the same in all times and places," that although Europe is the single best civilizations, he noted, "all humans could achieve and enjoy" the same degree of superiority if they're willing to learn. There were also George Forster, who argued universalism but still recognized local differences.
But in 19th century, statements such as this from Georges Cuvier seem to be more common,
There are ... certain intrinsic causes which seem to arrest the progress of certain races, even in the most favorable [environmental] circumstances. ... The civilization of the Mongolian race had remained stationary and that Negroes had never progressed beyond utter barbarism.
What happened in a century? What theological and philosophical paradigm changed?
Hey, I asked a very similar question about race and the development of racism a while back. It's not directly what you're after but you might be able to find what you're looking for here, in this comment by /u/medieval_pants and throughout the thread.
I cannot provide the whole answer as I do not know much about 19th century racial attitudes, but I do hopefully have some idea of why Europeans often had non-exclusionary attitudes to different races in the early stages of colonisation and exploration.
The idea of a universal political/societal bond between humans was one of great interest to thinkers in the 17th century. Some historians have argued that this idea had increased relevance after the reformation, as people tried to conceive of how their societies could stay together despite the increasing religious differences between them.
Some conceived of this bond as being allegiance to one's secular sovereign power, regardless of religion('rendering unto Caeser), others noted how even pre-Christian people had respected the power of a solemn oath, and held that this meant God had intended religiously diverse people to trust each other on the basis of bonds, oaths and covenants.
Some argued that 'civility' was the universal force which united people: despite their cultural and religious differences, if people could treat each other with mutual respect, peace could be achieved. This civility was seen as necessary for participation in Godly society, and therefore treating native Americans with respect was seen by some as a necessary precondition of their conversion to Christianity.
Also missionary work, when undertaken by Protestants, often involved the cooperation of various heterodox flavours of Protestantism, with people actively encouraging this as a way of promoting Christian unity. Therefore spreading of Christianity had to be promoted in an 'inclusive' and 'civil' way as a. it was seen as most conducive towards conversion and b. to approach it otherwise would have undermined its purpose of uniting dissenting Protestants.
My point here is that Europeans, particularly Protestants, were due to their own political and religious circumstances rather preoccupied with developing theories of man's universal nature. This often had connotations of an inherent Godly moral good, or at least a common understanding of civil behavior and binding political bonds, which meant all people, regardless of religion or race, could in some sense participate productively in society.
I should stress of course that this is to by no means suggest that all interactions between European and non-European people in the 17th Century was 'positive' or 'respectful', this clearly wasn't the case, but that attitudes were varied and did not always see non-Europeans as inferior, even when they saw them as religiously unenlightened.
How and why this had changed by the 19th century I can't say, as I say its not really my period. My hunch would be that a lot of the ideas of divinely inspired universal characteristics of the human race which were common in the early modern period were undermined by the greater prominence of naturalistic conceptions of reality and more non-interventionist conceptions of God during the 19th Century. Combined with the development of ideas about natural selection and evolution, this meant ideas which in the past had served as a check on people's prejudices had in some cases been replaced in popularity with ideas that fueled them. However as I say there is probably a lot more to it than this and it would be great to hear from someone with greater knowledge of the 19th C.