First of all the passage from John about the adulteress woman is not part of the original text of John. It was added. Secondly Jesus was not opposed to stoning. He was opposed to stoning on the basis of a sinful witness, since a witness who is conducting a sinful witness procedure cannot be trusted.
Jesus in the gospel said love your neighbor as yourself. He also said we should hate our own soul luke 14:26 "26 If any man come to me, and hate not his father, and mother, and wife, and children, and brethren, and sisters, yea, and his own life also, he cannot be my disciple. "
So if one should love your neighbor as yourself but hate your own life, then you should hate your neighbors life as well, just as Jesus said to hate your family too.
Secondly the gospel of matthew is the least reliable gospel in my view, containing the most editorial to impose a foreign morality into the text. the point Jesus was making is that eye for eye is not a justification for taking the law into your own hands and not a justification for punishing people because they "deserve" it. Eye for an eye is about true justice. And true justice also requires not harming others without justification and authority. Jesus was an extremist orthodox Jew. Not a new age pacifist gnostic.
Luke 19:27 "But bring here those enemies of mine, who did not want me to reign over them, and slay them before me" luke 17:2 "It would be better for him if a millstone were hung around his neck, and he were thrown into the sea, than that he should offend one of these little ones."