"It is logical to think that the Nazca people's religious beliefs..." would be easier to accept without the word "religious." Does anyone else see an assumption in all this? Building on assumptions is NOT logical.

It really is not an "assumption" that the Nazca Lines and geoglyphs served a religious purpose for the ancient Nazca's. There is plenty of circumstantial evidence that strongly suggests the Nazca Lines, and indeed other geoglyphs in other parts of the world such as Ohio's Great Serpent Mound, were a form of religious art created in response to the total solar eclipse "Eye of God". Thus it is perfectly logical, not just an unfounded assumption, that these geoglyohs served a religious purposes and probably were sites where religious rituals of various kinds took place.

:We need a parallel term for "anthropomorphization," one meaning to turn populations into religious believers. How about "paganization"? (verb nov., to make pagans of). Maybe the term "othering" is adequate.

Well most of the religious believers of that time period were "pagans" as it were. ;-)

:Why can't non-historical actors be scientists or free-thinkers instead of priests? Is that too illogical?

It is not illogical if there is clear evidence that they were scientists or "free-thinkers". Then again why can't "free-thinkers" be religious? I dare say that the Nazcas and other cultures were "free-thinkers" in developing their religious beliefs. Likewise there is no question that their "priests", or whatever other word you choose to use, were also "scientists" in that they clearly developed and made use of scientific astronomical knowledge as part of their religious practices.