Well, at first glance they appear completely opposed to each other. The society of Waknuk is implacably opposed to any form of "deviations" as a result of the Tribulation and the subsequent nuclear fall-out, so much so that any human that is classified as a "deviant" is neutered and then expelled into the Fringes, which of course is the unfortunate fate of Sophie, David's childhood friend, in spite of her parents' best efforts to prevent her "deviation" coming to light.
So in a sense, the philosophy of the Waknuk community has created the Fringes. However, when David, Rosalind and Petra are captured by Fringes men towards the end of the story, they see how the Fringes people are implacably opposed to the Waknuk community, no doubt driven by the personal enmity of Gordon the "spider-man" for his brother, David's father, and for the way that he was disinherited because of his deviation.
So, although there clearly are differences along religious lines and attitudes to deviation, both groups seem to be motivated by hatred of the other, as shown by the frequent incursions of both sides into the territory of the other, for example, when Gordon was captured towards the beginning of the book.