As an occult practice, it may have been discouraged at least, but to say "non-Christian" makes it sound like one arbitrary practice extirpating another.
Rather, the Christian view (and certainly the Catholic view) is one opposed to superstition and the occult on the grounds that superstitions are irrational and immoral and thus opposed to the good of those who engage in them[0].
It is one thing for there to exist varying customs that are more-or-less arbitrary w.r.t. the signifier (greetings, for example), but the signified is no longer arbitrary.
As a Catholic, even I recognize that essentially the entirety of Catholic practice is superstition from the perspective of anyone who doesn't either take Catholicism as a priori true on authority or (arguably equivalently) have a personal divine experience justifying Catholicism experientially.
If one is not Catholic to start with, it as easy to dismiss Catholic practice on the same argument as presented above against superstition as it is for Catholics to do so for non-Catholic superstitions.
While the foundational tenets of Catholicism are supernatural but the system that sprouts from it is highly rational, descriptive and formal. It's a religion of Roman lawyers and it shows.
As a result I have a hard time seeing anybody dismissing Catholicism as superstitious, even if they a priori dismiss the existence of God, unless they have no actual knowledge of it (which, you know, ends up being most people who feel to need to utter an opinion on the subject).
Catholicism teaches that the laying of hands can endow a person (of male biological sex) with the power to transform bread and wine into flesh and blood through the ritual utterance of certain words.
It's going to be hard sell to explain how that's not superstitious...
I guess I see what you mean by a religion of Roman lawyers...
To the Aztecs, presumably, there was nothing superstitious about using obsidian mirrors as a shield against evil sprits, either.
Also, the belief that praying to someone who was executed two millennia ago would bring you eternal life in Heaven is as superstitious as you can get.
Yes, with the minor complication that a substantial number of Catholics don't actually understand how it's supposed to work (spiritually speaking) and would be absolutely dumbfounded at the basic concept of transubstantiation.
According to doctrine, it's more than symbolic: Catholicism teaches that bread and wine 'really' turn into flesh and blood, while only 'superficially' maintaining the appearance of bread and wine (cf Aristotle's substance theory and the difference between essential and accidental properties). So under a certain point of view, the Eucharist could indeed be considered cannibalism - however, the body of Christ is divine and cannot be digested...
https://www.newadvent.org/cathen/12734a.htm
In any case, the conquerors of New Spain did not encourage the Nahuas to reform their indigenous religion on a rational basis free of superstition. They did not train up an Aquinas for Tezcatlipoca. They suppressed the religion of their conquered subjects in favor of their own, a tale as old as written history.
Yes, because that's exactly what it was. If anything they could stand to emphasise the hypocrisy a bit more, though I don't think that was particularly relevant to their actual point.