The similarities between the philosophy of the Waknukians the dwellers of the fringes is similar in that both groups of people think that they have the correct understanding of what God is doing and how he views what is happening in the world. The Waknukians feel that they are the final form, God's intended form the the human, and that they must zealously defend that form and stamp out any deviations from it. The fringe dwellers, as the man who takes David to his uncle testifies, believe that God does not have a final form at all, and that he is continually trying to develop and change the human form into something better and purer. As David says after hearing this belief, it is confusing how many different views about God and his workings in the human species there are:
It was odd, I felt, how many people seemed to...
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have positive, if conflicting, information upon God's views.
The similarities in the philosophy of these two groups of people therefore lie in the way that both of them think that God is acting in humans, and that they both believe they understand how God is acting and that the other group is wrong.
In "The Chrysalids," how are Waknuks and Fringe people's philosophies similar?
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.