Tutu is making a peculiar claim here, and I can't entirely tell if he's serious. He says they weren't motivated by politics, but by the Bible; but then he says the Bible was subversive. Does he mean that it was politically subversive, or is he talking about some other kind of subversion - spiritual or moral or psychological subversion, perhaps? I guess the question is this: what exactly was being subverted? He says plainly that it was "injustice and oppression." But what is not so plain is whether the injustice and oppression were primarily political; or if the political was only a sign or symptom of something else.
I've also been reading a lot of William James this week, especially The Varieties of Religious Experience. James argues that we should not judge religion a priori but rather a posteriori. As James puts it, "not by its roots, but by its fruits."
In that book and elsewhere, James argues that we are wrong to think that reason's chief role in religious experience is to judge the truth-claims of religion. Rather, religion is to be understood as playing a role within reason itself. Religion "is something more, namely, a postulator of new facts as well" as being a means of "illumination of facts already elsewhere given."
James and Tutu both offer religion as more than simply another second-string player on an already deep bench, and as more than a degenerate form of political reasoning. For both of them, religion is a source of insight that cannot be had in other ways.