For the purposes of this question, take the Cultural Relativist Thesis to be the claim that what actions are right and wrong is a function of the which actions the norms of one's culture endorse as right and condemn as wrong.
Say that that thesis works for a member of an isolated and culturally homogeneous hunter gatherer cultural group. For members of contemporary "modern" societies, there seems to be a problem that does not arise for the members of isolated and homogeneous groups.
We all are members of multiple cultures at one time. Consider, for example, a liberal Catholic native French-speaking resident of the Canadian Province of Manitoba. She belongs to Canadian, Manitoban, Francophone, Franco-Manitoban, Catholic and liberal Catholic cultures. She likely also belong to other subcultures based on her profession and hobbies. On at least some moral issues, these various cultural affiliations will pull in different directions. For instance, overall, Canadian culture supports same sex marriage, Catholic culture does not, and support for same sex marriage is lower in the Prairie provinces (such as Manitoba) then the more populous provinces.
So, how do proponents of the Cultural Relativist Thesis respond to the difficulty that, for most people in the world, there is no one unique culture to which they belong and that the various cultures to which a person belongs may provide both the verdicts of "right" and of "wrong" for some particular actions?