That the Mexica killed people as a religious act is not in question. It is described in detail in Nahuatl-language testimony as well as in Spanish accounts, depicted in their own art, and confirmed archaeologically. Excavation in the main temple precinct of Tenochtitlan has recovered dedicatory burials, offerings containing human remains, and the platform that supported a rack of skulls, along with towers built from skulls. The remains include men, women and children.
What is disputed is scale and interpretation. The very large totals given in some colonial sources, including figures in the tens of thousands for a single temple dedication, come from writers with reason to present the practice as extreme, were often set down decades after the events, and are not supported by the osteological material recovered so far. Careful accounts therefore attribute such numbers to the source that reports them rather than asserting them, while accepting that the practice was frequent, public and central.
Interpretation has swung. Older writing often treated the rites as evidence of a uniquely bloodthirsty culture; a later reaction proposed material explanations, including a protein-shortage theory that specialists have generally rejected. Current work tends to read the practice in its own terms: as the discharge of a cosmic debt, as an extension of warfare in which the capture of an enemy rather than his death on the field was the objective, and as a public demonstration of imperial power over subject peoples whose gods and whose captives were displayed in the capital.
Two points are often lost. The Mexica were not unusual in Mesoamerica in practising human sacrifice, only in the scale and visibility their empire gave it. And the Spanish who recorded it in horrified detail were themselves prosecuting a war of conquest and conducting public executions and burnings, and their accounts served to justify both.