Hillary Rodham Clinton isn’t just running against Republicans. She’s also running against parts of her husband’s legacy. On issues large and small, the Democratic presidential contender is increasingly distancing herself from — or even opposing — key policies pushed by Bill Clinton while he was in the White House, from her recent skepticism on free-trade pacts to her full embrace of gay rights. The starkest example yet came Wednesday, when Hillary Clinton delivered an impassioned address condemning the “era of incarceration” ushered in during the 1990s in the wake of her husband’s 1994 crime bill — though she never mentioned...