The basic historical evidence is simple. There were false Christs, and they were confounded and punished. What else do we need to understand? First, this verse comes immediately after the removal of the Lamanites from the lands of Zarahemla, and one verse away from the "contentions." We will see in the next verse that there are contentions again, with the final assertion of Benjamin as a holy man who establishes peace. It would appear, then, that these false Christs are arising from his own people, and represent a significant division in opinions among the people about the nature of religion.
Benjamin's religion would be an anomaly in Mesoamerican religion - a denial of accepted deities and actions. We know that the Zarahemlaites had lost their religion, meaning that they had lost the Jerusalem religion. It is clear from this evidence that the melding of religious ideas was ultimately even harder than melding the cultural styles.
The next interesting aspect of Mormon's description is that there were false Christs. When we saw Sherem before Jacob, modern interpreters have labeled him an anti-Christ, not a false Christ. Mormon is writing much later, so we cannot be absolutely certain what was on the plates. What we have are Mormon's words in the 400's CE that Benjamin had to deal with false Christs. What might he have meant?
A false teacher or a false prophet is one who teachers a false teaching. While an "false Christ" would also teach false teachings, the problem is intensified in that the person himself is "false." In order to be a false Christ, the person must purport himself to be Christ. Remembering that Sherem denied the future Christ entirely, it is not really likely that there were those who were attempting to claim the status of this future Messiah. Only those within the Nephite religious tradition would have known enough to be able to present themselves as a "Christ." This would seem unlikely given the religious cohesiveness of the Nephites who fled Nephi and entered Zarahemla. The Zarahemlaites had lost their Jewish religion, and had not had the benefit of New World prophecies heightening the Messianic expectation. Something else would appear to be represented by the idea of "false Christs" this early after the joining of the Nephites and Zarahemlaites.
Although the term and culture far post-date the Book of Mormon, a possible explanation comes from the Nahua concept of ixiptla. "The Aztecs appear to have been a people compelled to insist on the visible presences of their gods. In the conceptualization of these presences they went to extremes of detail…But the Aztecs had a special type of idol which differed radically in that it was animate and incarnate. This was the ixiptla, "image" or "representative," a person who wore the regalia, acted out the part of the god, and then was sacrificed." (Brundage, Burr Cartwright. The Fifth Sun. University of Texas Press, 1979, p. 57).
There are aspects of the Aztec ixiptla that probably did not pertain to Benjamin's time, such as the final sacrifice of the deity-incarnate. However, the concept of the representation of the god's by donning the masks of the gods appears to have wide representation in Maya culture in the iconography. It may be that the term "false Christs" was appropriate because the persons were deity impersonators from the competing religions - people perpetrating the old religion by donning the regalia of the gods to continue in the old ways. This would certainly have caused a division - a "contention" in Zarahemla between the way of the newly entered Nephites and the old Zarahemlaites.