So, this is quite an interesting question actually. I'm not sure I can tell you a precise answer about the Aztecs, but I can tell you about Spanish attitudes regarding Native Americans in general. It is generally accepted that modern ideas about race had not really existed for the first century or so of colonization. What did exist was a much more fluid understanding of races and peoples, usually based on religion and culture.

To give you some idea of what I mean, we first have to grasp some understanding of the ways that early European settlers understood the New World in general. The two most popular ideas were that the New World was an Edenic realm where the people had not been touched by original sin, while the other, not so coincidentally, was a land where Satan had total sway over the people. Both of these views were religious at their core, but were polar opposites ideologically. The important thing, however, is that in neither views were the natives fundamentally unchangeable. A sinner can be saved and a Saint can fall, if you see what I mean.

Second, the Spaniards in particular and the Europeans in general did not see their own races as necessarily fixed. The ideas of the humors was current at the time with the idea that you had to balance the four humors to be healthy. This idea was complicated by the fact that outside factors, including environment, effected the necessary balance. So, the upshot is that many people thought that if you lived in a tropical place, such as most of Latin America and the Caribbean, you could literally turn into a person who looked like a native. This did not even have to happen over generations. The first Spanish settlers into the Caribbean imported, at great expense, foods that they would have eaten back in Spain, most notably grain which did not grow well in the new colonies. At the same time, they tried to limit the amount of corn (maize) that they ate since it would turn them into Natives. The flip side is that if Native Americans ate European food they could become more European. The question of Native wet nurses for Spanish children was also critical since the nurse could transfer her humors to the child. An interesting later corollary occurred in the British colonies as late as the eighteenth century where many people believed that having sex with an African person (Usually a white woman having sex with a black man. Let's play spot the sexism) would result in the white person literally darkening.

A related issue, which the Colonists explicitly and frequently invoked to justify colonization was the classic "good use of the land" argument. Most of Europe was heavily agricultural. They saw the lack of cultivation of crops that they liked, i.e. wheat, grapes, etc. as proof that the Natives were inferior to the Europeans. There were some attempts to "Europeanize" the Natives by giving them European clothes and teaching them how to cultivate the land like Europeans, but these efforts were often undercut by Imperial legislation, most particularly sumptuary laws. The efforts to make the Natives European also raised a tricky practical question. If these guys become like us, what is the justification for ruling them?

A final factor, also religious, is that slavery in the 1500s was primarily based on religion and war. Christians were not supposed to enslave other Christians, but Muslims, and frequently prisoners of war, were ok. Of course, it did not take long for the Spaniards to effectively enslave many Native Americans on the well known encomienda and in the Spanish mines that dotted Latin America. However, the Natives died off really fast and many of them had converted to Christianity as well, leading to both practical and theological problems with the arrangement. Bartolemeo de las Casas famously defended the Native Americans and attacked their treatment before the King, though he also famously suggested African slaves to do the labor instead of Natives.

Racial attitudes changed drastically during the seventeenth century, when more permanent notions concerning race began to develop. By that time so many Natives had died that they posed little to no threat and the importation of African slaves began to take off in a big way.

The upshot of all this is that the inferiority of the Natives was heavily weighted toward culture and religion, rather than a modern understanding of race. However, the exact degree of inferiority is a question in and of itself. Not surprisingly, opinions differed greatly. But, as the empire continued to expand and generate more profit, the Spanish (and later the other European empires) came up with other ideas to justify their rule, increasingly relying on race rather than religion.

Hope this helps answer your question!

Further reading: Earle, The Body of the Conquistador (probably the most applicable to your question), Block, Ordinary Lives in the Early Caribbean, De la Fuente, Havana and the Atlantic in the Sixteenth Century, Carmagnani, The Other West (This one is more a general history of Latin America, but it's good.)

18th Century Degenerates

/u/onthefailboat has given an excellent answer, and I want to reinforce the fact of our modern notions of race being fixed and intrinsic as something that developed in the centuries after (and in response to) contact with the Americas. It's not until the 18th Century that we see the solidification of the notions that would inform "scientific" racism and our own modern ideas of race, which is one that is primarily based on inborn qualities distributed on a geographic basis.

The Comte de Buffon, an important transitional figure, still believed that the physical markers we consider so important for race (like skin color and appearance) could change over a single person's life, depending on their behavior and diet. Yet, he also believed that humans were ultimately subject to their environment, and that the environment of the Americas could cause the degradation of any people living there. Part of this is because he thought the Americas were literally a new world, having arisen from the sea after Eurasia and Africa, and thus being a land of swamps and wetlands whose noxious miasma would degrade the constitution of any living creature subjected to those conditions. Buffon, like so many who cast aspersions on the Americas, never visited any part of the continents. His assertions of miasmic conditions giving rise to nothing but stunted and weak creatures was famously refuted by Thomas Jefferson sending him the stuffed body of a moose.

Cornelius de Pauw, coming a generation after Buffon and drawing heavily on his work, also relied on a theory of environmental degradation, and specifically the environment of the Americas as producing weak and malformed creatures. He took a more extreme view than Buffon though, for where Buffon claimed that climate led to the genitals of Native American men being small and poorly functioning, de Pauw hypothesized that all the men were functionally impotent, requiring the bites of insects to swell their penises for sex. The effect of the humid climate on Native American women, however, left them with such well lubricated genitals that babies slid from them easily and with barely a notice from them. The intellect of these people was also decried and de Pauw is infamous for outright dismissing any accomplishments of Native Americans and calling conquistador accounts lies, saying the depiction of Tenochtitlan as a grand metropolis was mere fantasy and that the palaces the Spanish wrote about were nothing more than huts. Keen's The Aztec Image in Western Thought, records a representative summation of de Pauw's view of the people of the Americas:

Is it not astounding to find half the world occupied by men without bears, without intelligence, tainted by venereal disease, and so debased that they are incapable of being trained -- a defect that goes hand in hand with stupidity? The inclination the Americans have laywas had for the savage life proves that they hate the laws of society and the restraints of education, which, by dominating the most immoderate passions, are the only means that can raise man above the animal.

De Pauw, like Buffon, never actually visited the Americas. The popularity of de Pauw's extreme views, however, actually prompted Buffon to moderate his views and even write in defense of the achievements of Americans. The position of de Pauw, that Native Americans were fundamentally inferior and without achievement, would become the consensus among European naturalists. Cañizares-Esquerra's How to Write the History of the New World does an excellent job of tracing how the very same native works and oral accounts which the early Spanish based their works upon had, by the 18th Century, become evidence of the inferiority of Americans. He notes that a review of Clavijero's La Historia Antigua de Mexico, a book generally portraying the Aztecs as a civilized people (also, of note, the root of using "Aztecs" as opposed to "Mexica"), completely dismissed the work. The sources for the text were nothing more than "pictures either painted or wrought with party-coloured feathers" and that it was:

stuffed with impossible facts, absurd exaggerations, and such a barbarous jargon of uncouth names, as to to be within one degree of absolute unintelligibility."

Conquistadors and Virtuous Pagans

Notice, however, the de Pauw and his contemporaries placed on decrying the first-hand accounts of the conquistadors. The enmity to these accounts was not a mistake; they specifically contradicted his views. The Spanish who arrived in Mesoamerica in the early 16th century were functioning on a more medieval, even romantic, view of race which had significant differences from our modern view. Martinez's Genealogical Fictions makes the case that, while we cannot completely divorce the historical concept of race from our current interpretation, connecting the two views must be done cautiously and with acknowledgement that the 16th century worldview was one "strongly connected to lineage and intersection with religion." Thus, the early Spanish might have seen themselves as superior, but they bolstered that assumption with assertions of their Christian faith and genealogical accomplishments. There was plenty of room, therefore, to see the Mesoamericans as inferiors to be instructed in the ways of the Church, while also allowing for praise of their accomplishments and specifically of certain pagan rulers.

Cortés, for example, in his First Letter back to Charles V, does not disparage the intellect or accomplishments of the Americans, but instead spends a great deal praising their art and architecture before moving on to decry their pagan customs. He finishes this section saying:

your Majesties may reap great merit and reward from [God] in sending the Gospel to these barbarian people who thus by your Majesties' hands will be received into the true faith; for from what we know of them we believe that by the aid of the interpreters who should plainly declare to them the truths of the Holy Faith and the error in which they are, many, perhaps all of them, would very quickly depart from the their evil ways and would come to true knowledge, for they live more equally and reasonably than any other tribes which we have hitherto come across.

Though Cortés, in his letters, is famously kissing the ass of the Spanish King in an attempt to justify his expedition and not be arrested, we can still see the fundamental disconnect between the Spanish and the Mesoamericans was, in his eyes, less a racial distinction and more a religious one. These were, in his thoughts, a people ready to receive the word of Christ and enter into the overarching brotherhood of Christendom. The civilizations he was encountering were inferior to the Spanish only inasmuch as they deviated from good Christian morals, yet were otherwise held in high esteem. Writing of the city of Tlaxcala in his Second Letter, he says:

The city is indeed so great and marvellous that though I abstain from describing many things about it, yet the little that I shall recount is, I think, almost incredible. It is much larger than Granada and much better fortified. Its houses are as fine and its inhabitants far more numerous than those of Granada when that city was captured. Its provisions and food are likewise very superior... There are gold, silver and precious stones, and jewellers' shops selling other ornaments made of feathers, as well arranged as in any market in the world. There is earthenware of many kinds and excellent quality, as fine as any in Spain. Wood, charcoal, medicinal and sweet smelling herbs are sold in large quantities. There are booths for washing your hair and barbers to shave you: there are also public baths. Finally, good order and an efficient police system are maintained among them, and they behave as people of sense and reason: the foremost city of Africa cannot rival them.

The Spanish, in other words, saw themselves as interacting with a society on parity with their own (though sadly pagan). Likewise, they saw the leaders of those societies through the lens of nobility. Xicotencatl and Maxixicatl, leading figures among the Tlaxcalans, were written about as wise and capable leaders, who provided good counsel and who would be "good and faithful friends to the death." Even Motecuhzoma, so often portrayed as weak and vacillating in later accounts, is painted as a wise and capable ruler of a magnificent land, who Cortés personally admired and liked.

Greetings travellers,

If you are a first time visitor, welcome! This thread is trending high right now and getting a lot of attention, but it is important to remember those upvotes represent interest in the question itself, and it can often take time for a good answer to be written. The mission of /r/AskHistorians is to provide users with in-depth and comprehensive responses, and our rules are intended to facilitate that purpose. If your post doesn't follow the rules, for reasons including unfounded speculation, shallowness, and of course, inaccuracy, it will be sacrificed to the gods. Making comments asking about the removed comments only increases Quetzalcoatl's thirst for blood. So please, before you try your hand at posting, check out the rules, as we don't want to have to carve at you with flint knives to please deities whose names we can't pronounce.

Of course, we know that it can be frustrating to come in here from your frontpage or /r/all and see only the lifeless remains of posts that now say only [removed]. We ask for your patience and understanding. Great content is produced on this subreddit every day, praise Quetzalcoatl the Winged Serpent, and we hope that while you wait, you will check out places that are pleasing unto Him, including Twitter, the Sunday Digest, the Monthly "Best Of" feature, and now, Facebook. It is very rare that the god is not appeased in due time, so please do come check back on this thread in a few hours. If you think you might forget, send a Private Message to the Remind-Me bot, and it will ensure you don't!

Finally, while we always appreciate feedback, it is unfair to the OP to further derail this thread with META conversation, so if anyone has further questions or concerns, I would ask that they be directed to the high priests through modmail, or a META thread. Thank you!