[1894 Scrivener New Testament - vs 1-11 were not included in later texts]
Jesus said that He did not come to judge. Later, Jesus will be the righteous judge, but at this time He came to "seek and save that which was lost." He was the only person without sin and, as such, He could have condemned her, but He didn't.
We are still in the time of salvation. "Today is the day of salvation." As such, we need to redeem and save until the day of judgment. We have no business judging and condemning others.
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Note: This does not mean that we don't recognize sin. Jesus told her to go and sin no more. He did not excuse her sin, He offered her forgiveness and salvation. Those who accept forgiveness but do not change their actions, will be judged at the day of judgment. To the unrepentant sinner, we may remove him or her from the fellowship of the church, but this is an extreme action and should not be taken without exhausting every way to resolve the matter first.