Rahm Emanuel has been a fixture in Democratic Party politics for more than 30 years — serving as a member of Congress, President Obama's chief of staff, mayor of Chicago and ambassador to Japan. He is now exploring a campaign for the presidency, an effort that seems designed to challenge some orthodoxies of that same party. He has argued that Democrats have the wrong focus on social issues, education and the economy. Appearing on a podcast with the conservative host Megyn Kelly, he answered a question about transgender people in a way she praised, and then he joked that he...