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In country after country across Europe, the Syrian refugee crisis has put intense pressure on the political establishment. In Poland, voters have brought to power a right-wing party whose leader, Jarosław Kaczyński, warns that migrants are bringing “dangerous diseases” and “various types of parasites” to Europe. In France’s regional elections in December, some Socialist candidates withdrew at the last minute to support the conservatives and prevent the far-right National Front from winning. Even Germany, which took in more than a million asylum-seekers in 2015, has been forced to pull back in the face of a growing revolt from Chancellor Angela Merkel’s own party and the recent New Year’s attacks on women in Cologne, allegedly by groups of men of North African origin.

And then there is Denmark. A small, wealthy Scandinavian democracy of 5.6 million people, it is according to most measures one of the most open and egalitarian countries in the world. It has the highest income equality and one of the lowest poverty rates of any Western nation. Known for its nearly carbon-neutral cities, its free health care and university education for all, its bus drivers who are paid like accountants, its robust defense of gay rights and social freedoms, and its vigorous culture of social and political debate, the country has long been envied as a social-democratic success, a place where the state has an improbably durable record of doing good. Danish leaders also have a history of protecting religious minorities: the country was unique in Nazi-occupied Europe in prosecuting anti-Semitism and rescuing almost its entire Jewish population.

When it comes to refugees, however, Denmark has long led the continent in its shift to the right—and in its growing domestic consensus that large-scale Muslim immigration is incompatible with European social democracy. To the visitor, the country’s resistance to immigrants from Africa and the Middle East can seem implacable. In last June’s Danish national election—months before the Syrian refugee crisis hit Europe—the debate centered around whether the incumbent, center-left Social Democrats or their challengers, the center-right Liberal Party, were tougher on asylum-seekers. The main victor was the Danish People’s Party, a populist, openly anti-immigration party, which drew 21 percent of the vote, its best performance ever. Its founder, Pia Kjærsgaard, for years known for suggesting that Muslims “are at a lower stage of civilization,” is now speaker of the Danish parliament. With the backing of the Danish People’s Party, the center-right Liberals formed a minority government that has taken one of the…