If you take the definition of science fiction to be something like fantasy but still bound at least loosely by scientific principles as they are currently understood, much of the larger plot elements certainly fit. The nuclear wars that mark the beginning and the ending of the story are well within our current level of understanding. As are many of the mutations and changes that take place within some of the characters like the two headed woman, etc.
One of the other ways that the novel fits with the definition of science fiction is that it involves a "dystopia," a society in which the normal rules have changed or been broken down. The incredible combination of scientific oddities and religion and the way they are melded together in the story are ways that the novel fits the definition.