I am sympathetic to you because this is a convoluted question that seems to have very little to do with what Hurston is talking about in "How It Feels to be Colored Me." However, one could read her personification of God as "the Great Stuffer of Bags" with the sense that the contents of brown, red, yellow, and white bags—just as the contents of brown, red, yellow, and white bodies—carry different things based on both heritage and personal experience. All of the bags, or bodies, "contain" different things, such as Hurston's deep feeling for jazz versus her white friend's relative indifference. Even so, one also has to take into account Hurston’s belief that the contents of the bags are largely the same, regardless of their colors, and that God may have intended this resemblance:
In your hand is the brown bag. On the ground before you is the jumble it held—so much like the jumble in the bags, could they be emptied, that all might be dumped in a single heap and the bags refilled without altering the content of any greatly. A bit of colored glass more or less would not matter. Perhaps that is how the Great Stuffer of Bags filled them in the first place—who knows?
It would be possible, if you insisted, to connect the differences tied to the "colored glass" and bags (rather than the vastly more important similarities Hurston sees between people) to essentialist arguments about race, which have been made throughout history. For example, there has been a long-held belief that black people are more passionate and more attuned to music and dance than whites. There is no scientific evidence for this, but the belief is drawn from differences in cultural conditioning. Indeed, West African religious rituals included dance. The slave descendants of these West Africans, who were assimilated to Christianity, incorporated dance into their form of Christian worship.
As for the use of religion to explain how different races came to be, there is the old belief that black people are the "sons of Ham"—or the cursed sons. There have been a myriad of justifications among racists who have called themselves Christians to justify their racism. Racist beliefs have also been based on pseudoscience, such as measuring skulls to determine intelligence. These are some religious and secular examples of how ideas about race has been tied to larger systems of belief, as your teacher says. However, these arguments directly oppose Hurston’s essay, in which she rejects such notions, as well as the idea that her race is a condition:
I am not tragically colored. There is no great sorrow dammed up in my soul, nor lurking behind my eyes. . . . No, I do not weep at the world—I am too busy sharpening my oyster knife.