So Jesus acknowledged her sin, and didn't excuse it, or call it not sin...but as God He forgave her, contingent upon her sinning in this way no more, i.e. her repentance.
It is fascinating to me how so many post-moderns skip the forgiveness and repentance part when telling this story.
Without that the, "neither do I condemn you" makes no sense at all.
Back to the subject: There is no indication that Dr. King repented of either his adulteries, nor his disbelief in Christ as Savior and Lord.
If Jesus is God then he had the right, to forgive and say sin no more. He was without sin.
But he does not expect YOU to judge.