Once again, something much more than the denial of the atoning Messiah is the message of the competing religion.
There could not be that many flattering words that would deny the mission of the atoning Messiah and retain everything else - and still lead people to "commit many sins." As Mormon indicated, there is a total rejection of the word of God, with the very specific rejection of the atoning Messiah. This alternate view of the world would certainly lead to a difference in practice due to the different understanding. These differences could easily be seen as sin, and require that they be "admonished by the church."
To understand how differences can lead to "sin," we should examine some of the types of things that might be altered. In the Mesoamerican context, the shift to a more Mesoamerican religion would require a shift in the nature of understanding God and the way the world works. This could lead directly to a significant difference in sacrificial practice. While the conception of sacrificial offerings would be common, the reason for the offering, the being to whom it was offered, and the nature of the offering would all be significantly different. For a monotheistic people, this was clearly sin to offer to a different god.