Lester del Rey’s The Eleventh Commandment: A Novel of a Church and its world is a standalone population-bomb novel. My edition is the revised 1970 edition.
A tragic mishap during a program of world nuclear disarmament led to the very nuclear war that the program was intended to prevent. As lethal fallout covered the Earth, sparing only a few lucky refugia, American and Russian spacemen1 created a new society on Mars. Mars became a high-tech utopia, populated by a eugenic elite, whereas Earth was left to stew in its own juices.
Boyd Jenson believes he has been sent to Earth to study there, a kind attempt to salvage his academic career after his long illness. In fact, the government of Mars has quietly decided Boyd does not meet Mars’ exacting genetic standards. He is not a transfer student. He is an exile. Boyd only discovers this after he is stranded on Earth, far too late to escape his terrible fate.
North America is a particularly dire part of a battered world, thanks in large part to the American Catholic Eclectic Church.