"The real question is whether you can regard these differences within a framework of progress—in the sense that some cultures, or features of culture, are better than others. The real question of cultural relativism, is one whether you think progress implies, as you said, an underlying innate sense—for instance a sense of justice—or whether these cultural choices are wholly arbitrary with none being better than another?"
This issue of cultural relativism is especially relevant in schools, though it is danced around (sometimes)—but the crux of it in essence is the question: Are some students' cultural backgrounds more conducive to learning than others?
I am not opposed to the question, but I think the premise is profoundly wrong-headed, and here is why:
The imminent advantage of teachers in the ever-increasingly volatile "culture wars" is that cultures revolving around pedagogy (i.e. the culture of/in schools) have a fixed basis to justify good/bad & right/wrong—and that fixed basis is teaching; the outputs of which are determinative... in fact, narrowly determinative... meaning that a school culture is driven by the task of teaching. School culture is a social tool that supports good teaching. The fixed basis is, of course, student engagement and more specifically, students' cognitive engagement. If this outcome is visible, the objective of pedagogy has been accomplished. Schools that prioritize this determinative basis for culture are more likely to have it affirmed in the achievement, experiences, and relationships of students within the school community.
There are notions regarding cultural relativism that are quite interesting material for theoretical debate. Often, I hear teachers asking (directly or indirectly) questions regarding the culture of students which often imply (or express explicitly) that some students are culturally deficient in relation to others—but these are precisely the wrong questions to ask. The better questions, the more pragmatic and productive questions, are about the culture of schools. All students have cultural fluencies which they bring to bear, and it is human nature to assess those whose culture is most similar to one's own as that which makes the most sense and is thus most desirable. But culture is merely the norms and fluencies we use in social contexts to make sense of the world. Teaching that effectively leverages culture engineers opportunities for students to use their cultural fluencies in order to build and bridge understandings with content. It is largely useless to critique another's culture because we can only understand culture through our own cultural lens. And what's more, culture is learned in the context of some determinative basis—as in, culture is acquired by individuals participating in social spaces with some intent. Culture is the sum total of the tools and ways of knowing that allow one to successfully participate in specific cultural environments.
Schools are dynamic cultural spaces in that many different backgrounds are represented. There is a specific fixed basis, however, that should be employed in evaluating the culture of schools. The fixed basis is student engagement. If students are engaged in rigorous intellectual exercise, the determinative objective of pedagogy has been accomplished. The comparisons of students' cultures are generally an inefficient use of teacher time and effort; it makes much more practical sense to investigate students' culture for the purpose of improving the pathways and strategies for bridging students' identities with the concepts we want for students to learn. All other considerations are speculative and subjective.