Hello! In 'The Chrysalids,' we learn that both David and Sophie belong to a religious totalitarian society. David lives in Waknuk, which is situated in Labrador. This society lives by a strict set of rules, designed to prevent yet another 'Tribulation.' It is intimated that God sent the Tribulation (nuclear holocaust) on the 'Old People' to punish them for their insubordination and their love of technological advances. The Badlands have the highest radiation levels, suggesting that the nuclear holocaust is devastating; the Fringes support no known forms of life.
We read that the people of Waknuk live by the Bible and a book named Nicholson's Repentances. All members of the society must live in such a way as to gain back the grace of God; deviances from the norm are not to be tolerated. All must conform to the strict rules. So, this society is one fraught with fear, distrust and suspicion. Anyone or any animal that is slightly different are termed Blasphemies or Deviations/Mutations, which are Offenses). This leads to severe culling, to ultimate death. David's knowledge about Sophie's extra toes puts him in danger. She is an anomaly: by right, he should be reporting her to the authorities instead of keeping her secret to himself. When David discovers that he has the gift of telepathy, even his Uncle Axel warns him to keep his abilities to himself.
This closed and superstitious society subjects both David and Sophie to possible persecution. Waknuk is representative of the type of prejudice and bigotry which has contributed to our modern WWII Holocaust of the Jews, the Armenian Holocaust, the Rwandan genocide, and the Cambodian genocide, to name a few.
So, you can see that David and Sophie's identities are shaped by the intolerance of the society they live in; they have to learn to keep deep secrets, in fear for their very lives. In this society, even parents and children may not trust in tender familial bonds; the 'rules' supercede all such loyalty. We see that David is afraid of his own father, the fanatical religious leader, Joseph Strorm. Joseph beats David severely for saying that if he had an extra arm, he wouldn't have to worry about injuries. Later on, he also beats David when he finds out why David spends a night at Sophie's home. David's own mother refuses to aid her own sister (David's Aunt Harriet) in keeping her Deviant child a secret and Harriet is subsequently found dead.
David wants to escape to a place where he, Sophie and Petra are not considered deviants simply because they possess a gift deemed a blasphemy by the society they live in. He has to teach Petra to control her power so as to escape detection by those who would turn her in. While Waknuk causes them to live in fear, it also cements their resolve to live freely away from such persecution.
How did it shape their identity and why did it shape their identity??
The society shapes David and Sophie's identity through intimidation and persecution, for the purposes of populace control.
Thanks for the question! If you are interested in a couple of summaries, I list the links below.