The refugees are arriving on a continent that since World War II has become home to a third of the world’s immigrants. Europe’s major countries, which once sent their huddled masses to the United States, now have foreign-born populations comparable to that of the United States. But only some European minds and fewer European hearts have adjusted to that reality. Even in the U.S., which John F. Kennedy called “a nation of immigrants,” immigration is a divisive issue—and always has been. In the 1750s Benjamin Franklin worried that too many Germans were coming to Pennsylvania. He said they had a...