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This book was about a girl who lived in a post nuclear society where they worshipped nukes. She was considered ugly, gangly, and tall - and had telepathic abilities. She is accused of witchcraft and she and a young boy have to escape through a wasteland filled with mutants. There are people from a more advanced society who are telepathically in contact with her and trying to rescue her and the boy.
I read it circa 1980.
This reminds me of Children of Morrow (1973), by Helen Mary Hoover.
It's set after an environmental disaster has wiped out most of humanity; the majority of the story follows a couple of children in one of the surviving towns who are in telepathic contact with another group of survivors. They end up having to escape into the wilderness to try and get rescued.
It's been quite some time since I read it, but a quick look at the article above says that the children's community worships one of the surviving nuclear missiles.
Another review here.
That sounds a bit like The Chrysalids (1955) (aka Re-Birth) by John Wyndham.
Blurb from Penguin:
David Strorm's father doesn't approve of Angus Morton's unusually large horses, calling them blasphemies against nature. Little does he realise that his own son, and his son's cousin Rosalind and their friends, have their own secret abberation which would label them as mutants. But as David and Rosalind grow older it becomes more difficult to conceal their differences from the village elders. Soon they face a choice: wait for eventual discovery, or flee to the terrifying and mutable Badlands. . .
