This is a pretty big question, and you're mentioning different centuries here, from antiquity to modernity. As the Enlightenment seems to be your main focus I'll try and focus on that. The first thing to address is the idea that European societies would somehow grow more tolerant or "enlightened" over time, and try to understand non-European societes on their own terms. While this did happen (I'll mention exceptions like Montaigne below) there are actually many ways in which Enlightenment thought became less tolerant and more fixed with an increasing focus on empiricism. As you rightly mention, we can even see a stronger development in the 19th c. with stronger possibilities of using rational science to show the supposed "inferiority" of other people, and also to show how their faiths in some ways actually came from Europe/Christianity. We should also keep in mind that connecting other belief systems to Christianity has always been a convenient way of drawing the unknown into a familiar (Christian) universe; and of showing the universal appeal of Christianity.

Canizares-Esguerra has done interesting work on the Enlightenment, although his main focus is on Europe and Latin America rather than Asia (in "How to write the history of the New World"). In this context, he first looks at European scholars writing about Latin America in the 16th c. At that time there was of course heavy discrimination against native people (and their beliefs) in their writings, but also a willingness to accept native ways of storing knowledge. This he than contrasts to a current of thought from the mid 18th c. onwards, with influential works by scholars like De Pauw, Robertson and the Abbé Raynal, who described native (American) people as clearly a "less civilized" people, including some pretty harsh characterisations. Voltaire and before him Montaigne can actually be seen as rather exceptional in this climate in their willingness to see native American cultures not as less developed, but as having reached (with the Inca and Aztecs) at least a comparable level of development to European civilisations, if not higher.

I hope this doesn't lead to far away from your question, as I'm esp. interested in Latin America. It still seems relevant to me as to show a less tolerant attitude developing towards other people in Enlightenment thought in comparison to the 16th/17th c. Turning towards East Asia, I think it's interesting to add that Voltaire and other philosphes drew heavily on Jesuit writings as the main sources on Chinese society and beliefs.

These portrayals were in turn of course informed by the necessity to show the great possibilities of conversion offered in China that did not exactly fit with reality - conversion was an extremely slow process in the 17th c. and the 18th cs. To do this, starting with one of the earliest Jesuits in China, Matteo Ricci, Confucianism was highlighted in favor of other schools of thought like Daoism, as it was seen as more comparable with Christianity (which is propably were the Jesuit Kircher got some of his ideas on this as well); and as you said parallels between Confucianism and Christianity were sought, although allowing Chinese religious rituals to be carried out by Chinese Christians at the same time. We should also keep in mind that thinkers like Voltaire used their writings on China, esp. on the Chinese emperor's sovereignty, to criticize misgivings on political developments in their own time. Towards the late 18th c. we can then notice a less positive portrayal of CHina in Europe, connected among others to changing trade policies, and expressed once again by Enlightenment scholars like the less tolerant De Pauw.

I'd like to get a bit more concrete here to show arguments and tactics used by Jesuits in China. Main strategies included knowledge of Chinese/mandarin and the adaptation of the Confucian elite's etiquette. Regarding propagation of Christianity and evangelization a "from the top down" strategy was using focusing on the emperor and elites. And indirect propagation was seen as useful by showing the superior value of European sciences and technology that would suppesedly also show the Christian religion's superiority. The openness towards Chinese values manifested itself in the tolerance of Confucian rites I mentioned, which included ancestral worship and veneration of Confucius. A return to original Confucianism was also propagated by the Jesuits, seen as more fitting with natural law. While these tactics did not yield the hoped for large-scale conversions, they surely functioned as a lens through which both Jesuits and Enlightenment philosophers who followed their works saw Chinese beliefs. On the other hand, the debates caused by Jesuit writings in French intellectual circles have also been described as contributing to 'break-ups' in encompassing notions of religion in Europe. Thus a focus was being laid not on religion and morality or religion and history, but rather on "religous and non religious spheres". Such debates can be seen as influencing the increasing importance of rationality and laicism in European thought.

Lastly I want to add a bit on South Asia. Here I'd esp. highlight the East India Company's and later the British Crown's administration's very selective focus on specific hindu writings; and their strong cooperation with the religious caste group of Brahmans who of course underlined their own supreme importance in religious matters. My professor used to argue that (as in other regions) it was the British influence that actually led to the grouping of various schools of thought and philosophies into a "religion" called hinduism - "religion" as a concept being introduced by Europeans who applied their own Christian preconceptions to the belief systems they encountered. As I said above, such developments became only more pronounced in South Asia in the 19th c., with the introduction of Christianity and the rise of the "New Imperialism" (on a slightly related note, I wrote about the British influence on the caste system here).

I kind of jumped from topic to topic here as your question is quite wide-ranging. What I wanted to underline though is: That molding various non-European belief systems into a monotheism recognizable to Christian beliefs in not an Enlightenent development, but built on much older European traditions (similiar tactics can be observed with 16th c. writings on native Americans); that such tendencies increased from the mid-18th c. following an increasing focus on empiricist "proofs" of European "superiority"; and that portrayals of European scholars built on highly partial sources ranging from Jesuits in East (and South) Asia, to Brahmans choosing sources that most fit their own purposes. These tendencies would inform later European scientific practices that, through a focus on rational, non-religious thought could claim a different degree of authority.