It is important to recall when analysing Black Beauty that Anna Sewell gave a statement of intent about why she wrote the story. She did not have bettering the lives of humans through religion in mind. She clearly had the aim of bettering the lives of horses in mind. In a statement, she declared that before she died she wanted to write a story that would "induce kindness, sympathy and an understanding treatment of horses" as the direct aim and goal. This indirectly involves humans as they are generally the ones who are responsible for how horses are treated.
Having said this, the precepts of kindness, sympathy and understanding are precepts embraced by religions, including Christianity, which would be the form of religion dominant in England during the period of the setting around 1870. These precepts are shown most fully in Chapter 36, "The Sunday Club," in which Jerry explains "true" and "real religion" and the one way to "make the world any better":
"If some men are shams and humbugs, that does not make religion untrue. Real religion is the best and truest thing in the world; and the only thing that can make a man really happy, or make the world any better."
These precepts of religion can be seen, then, as the undergirding that shapes the narrative as Sewell builds a story to show humans how to be kinder and truer and more sympathetically understanding so as to "induce kindness, sympathy and an understanding treatment of horses."