Unfortunately, I think Christ left a mixed message. For those of us who wonder about whether the death penalty is appropriate, John 8 seems to support our belief. He actions clearly spared that womans life from what was believed to be the remedy for her sins under the law. For those who believe that Paul's discussion of the civil laws in Romans (where I believe he does draw a line between civil and Christian) and the fact Christ was mute on the cross when hung with the two thieves with regard to the penalty, they hang their hat on those passages.
Again, a mixed message.
I'm not sure what Jesus was teaching at the time he addressed them was "the death penalty is wrong".
When Jesus said to the woman "neither do I condemn you"... I think he was speaking to her on a spiritual plain. A "kingdom of heaven" plain. I don't think any part of that lesson was pertaining to the death penalty for murderers.
Not civil and Christian. But Civil and personal.
The Jews could not legally put the woman to death as they had no civil jurisdiction.
Genesis 9:6 was written by the One know as the Spirit of Christ.
No contraditction; no dilemma.