The Rev. Al Sharpton once epitomized New York’s bad old days of the 1980s, when the then-corpulent, gold-medallion-bedecked tub thumper inflamed racial hatred and courted violence. Today, against all expectations and at least 100 pounds lighter, he has been rehabilitated into the Democratic Party’s civil-rights leader of choice. Has Mr. Sharpton changed or simply outlasted his critics?

President Obama’s embrace of Mr. Sharpton has been particularly intense this year. On Monday he called Mr. Sharpton’s radio show to discuss...