The "1/16 Cherokee" example seems to be clumsy adaptation of social techniques for trying to connect via commonalities. The intent counts for a bit. It certainly isn't effective or pleasing to the target, but it is an attempt to bridge and group-identify. That they aren't unconnected strangers with no link.

Arguably this a symptom of other conceptual issues (like needing genetic connections for kinship as opposed to universals). But it is a step of progress and a reason to educate rather than shun or scorn.