As the Seventh U.S. Army prepared to seize Axis-held Sicily in July 1943, Gen. George S. Patton sent the troops a message. “When we land,” Patton said, “we will meet German and Italian soldiers whom it is our honor and privilege to attack and destroy.”

Patton is famous for his martial exhortations, but Stanford historian David M. Kennedy paraphrases his Sicily address to highlight what it said about immigration. “Many of you have in your veins German and Italian blood, Patton said, “but remember that these ancestors of yours so loved freedom that they gave up home and country to cross the ocean in search of liberty,” whereas the Germans and Italians targeted in the Allied assault chose to remain “as slaves.”

The American soldiers Patton was talking to, Mr. Kennedy tells me, were “the sons of those immigrants who’d come 20, 30 years earlier.” A great wave of immigrants, mostly from Southern and Eastern Europe, had arrived in the U.S. in the late 19th and early 20th centuries, and Germans had been coming since before that. These groups “were thought to be unassimilable,” Mr. Kennedy says. Yet Patton effectively told them, “I’m counting on your being so assimilated that you can kill your ancestors or your relatives.”

The general thus colorfully rejected ethnic nationalism and gestured at an American creed that could encompass anyone committed to defending American values. Today, the 78-year-old Mr. Kennedy, author of “Freedom From Fear: The American People in Depression and War,” a Pulitzer Prize winner in 2000, sees this creed faltering. He worries that “in this big, throbbing, pulsing, kinetic, diverse society,” a sense of American “common purpose and common belonging” is being lost. Incompatible views of identity and immigration are fracturing politics.

“Societies that have deep, chronic, intergenerational ethnic differences inside the same body politic don’t have particularly encouraging histories,” Mr. Kennedy notes. “The basic human instinct to prefer one’s own kind to another is impossible, I think, to eradicate entirely.” That means forging “a coherent society out of people who are different in their origins and aspirations is a project,” and a fragile one. America’s capacity for absorption has been exceptional.

One early observer of American pluralism was J. Hector St. John de Crèvecoeur, a Frenchman living in 18th-century New York. In his “Letters from an American Farmer,” he asks, “what, then, is the American, this new man?” British settlers formed the core of the colonies, but Crèvecoeur “acknowledges all of the different peoples that have come to America,” Mr. Kennedy says, like “the Germans, and the French, and the Huguenots, the Dutch.” Crèvecoeur said “they all were melding their identities into this new creature under the sun.”

In the 21st century the notion that Crèvecoeur was even looking at a diverse society, Mr. Kennedy says, seems “kind of quaint.” Besides enslaved African-Americans, “they’re all Europeans, they’re all white, what’s the diversity here?” Yet this mix of nationalities was unprecedented in the Old World.

Mr. Kennedy doubts the “psychological distance” between groups in America is greater now than then. Imagine if we could compare the perception of Germans in 1785 to that of Poles in 1905 to that of Asian and Hispanic immigrants today. “My instinct is that the sense of difference is pretty comparable over time,” Mr. Kennedy says.

Then why are the politics of immigration so fraught today? One answer is polarization. As American identity fractures deeply into red and blue versions, new arrivals are losing a common ideal of citizenship into which they can assimilate.

Immigrants are also regarded by the political parties not only as workers or neighbors but as a voting bloc. Democrats tout America’s declining white share of the population as a key to their long-term governing majority; Republicans fear the opposite. Restrictionism on the right is rooted not only in cultural difference but also a fear that more immigration risks a loss of political power.

Immigration politics didn’t always sort neatly along party lines. During the wave of immigration between 1890 and 1914, immigrant votes were “up for grabs,” Mr. Kennedy says. “The political identity of immigrants and immigrant-descended communities really didn’t solidify” until the New Deal, after a 1924 law and the Great Depression reduced immigration. Franklin Roosevelt appointed a far larger number of Catholic judges than had the Harding, Coolidge and Hoover administrations. This showed that Democrats were “out trying to recruit loyalty in these immigrant communities, which were largely Catholic and Jewish.”

Mr. Kennedy sees today’s Republican Party as having all but “conceded that they will not make any inroads in immigrant communities,” as “nativist elements” in the GOP “seem to have gained the upper hand.” Yet the left’s changing approach has also made the politics of immigration more divisive. “In the last generation or two,” Mr. Kennedy says, “diversity became not just an observed fact, but something to be valorized in its own right.”

The dominant American view until the late 20th century was that “we welcome all kinds of people but we expect them to assimilate into some range of standard values, behaviors, aspirations, ambitions.” Now, diversity itself has become the paramount value in parts of American culture. When celebrating difference replaces creedal values like liberty, fair play and respect for the Constitution, that undercuts “the project of assimilation,” Mr. Kennedy says.

Diverse societies need stories, even myths, to articulate what they have in common or what they are working toward collectively. Mr. Kennedy suggests that academic historians no longer contribute to this national understanding. When he was trained in the 1960s, most historians agreed on a “master narrative about American history.” It was based on the “perfection of the idea of democracy of this country.” That process was “incremental, slow, back and forth” but you could “still trace the arc.” And it gave Americans a way to talk about their national project.

Academic history is dominated today by “subsidiary questions” about “ethnic or racial or gender” groups, Mr. Kennedy says. These are “all interesting and legitimate stories in their own right,” but they have “squeezed energy out” of “the big, integrative, long-term project.” He worries that “the history of America is no longer the history of America—it’s about things that happened in America. But the fact that they happened in America is kind of incidental to the story.”

Mr. Kennedy is clearly alarmed by Donald Trump’s anti-immigration politics. But from “a purely analytical or historical point of view,” he says, it should not be surprising. “There seems to be a threshold percentage of immigrants in the population that triggers a pretty robust nativist reaction. And the threshold,” based on the reactions in the 1850s, 1920s and today, “seems to be somewhere in the 11%, 12%, 13% range.”

Some trends suggest the reaction could abate. Mr. Kennedy says absorption in the early 20th century was accelerated by the fact that the immigrant stream “was highly variegated in terms of ethnicity, religion, language, culture.” The fact that “quite literally, Polish Jews could not talk to Greek Orthodox could not talk to Sicilian Catholics,” he says, reduced the sense of challenge to U.S. English speakers. By contrast, Hispanic immigrants exceeded 50% of all new arrivals in the early 21st century, with those from Mexico making up the majority.

Yet the immigrant stream has diversified once again in the past decade. Asia now tops Latin America as the No. 1 source of new arrivals. “Asia’s a big place, as Europe was 100 years ago,” Mr. Kennedy says, and “Filipinos and Chinese and Laotians and so on don’t easily fit into one cultural category.” In that sense “we’re returning to a more familiar historical pattern where immigrants come from a variety of places.” That could reduce political frictions that come with immigration. So would “consistent and robust economic growth,” Mr. Kennedy says, which “lubricates all kinds of social issues.”

If the American creed is exceptional in its ability to fold immigrants into its fabric, so it also is in its resistance to socialism, Mr. Kennedy suggests. He points to the German sociologist Werner Sombart’s observation that America’s early embrace of “more or less full political rights,” at least for white men, prevented European-style socialism from taking root in the 19th century. Despite the label’s brief revival in the Democratic primary, “my own view is that it still has a lot of toxic residue in big parts of the body politic,” he says.

Mr. Kennedy recently returned from a teaching trip in China, where the rules of national membership couldn’t be more different than in the U.S. The idea that one could “show up as blond, blue-eyed Irish German Caucasian and say, ‘I want to become Chinese,’ ” Mr. Kennedy muses—“the proposition kind of defeats itself as soon as you articulate it.”

The Chinese are deeply worried about “their integrity as a society and their coherence,” Mr. Kennedy says. “They’ve been ruled by outsiders for centuries in the Manchu dynasty,” he observes. They’ve faced severe “internal divisions, and the country has been fragmented and come back together, and fragmented again.” Asia’s geography adds to Beijing’s anxiety about social cohesion, given that China has “land borders or the near equivalent with 14 other countries.”

By contrast, the American story has been one of almost linear ascension. Its two neighbors are relatively weak and friendly, and it has only fragmented politically once in its 243-year history.

The ultimate manifestation of China’s drive for homogeneity is its treatment of the Uighurs in Xinjiang province. Mr. Kennedy visited Kashgar, a city in Xinjiang, though he didn’t enter the internment camps where more than a million Muslim Uighurs are undergoing “re-education.” Still, Mr. Kennedy says, “I could not have imagined a security surveillance state of that density and weight.”

“Every 250 meters, there’s a fortified police station,” Mr. Kennedy says. “Every intersection, there’s a little riot squad of cops, waiting to go. There are surveillance cameras everywhere, just absolutely everywhere. You go into a little noodle shop, mom-and-pop noodle shop, half the size of this room—you go through a metal detector, and there’s an armed security officer standing right there.”

Throughout U.S. history, the sense of what it means to be an American has been shaped by the country’s external enemies. Americans repudiated, or saw themselves as repudiating, monarchism in the revolution, imperialism in World War I, fascism in World War II and communism in the Cold War. Mr. Kennedy notes that “an adversary that is challenging enough” can “mobilize, and discipline, and focus, and even deprive citizens of certain things in order to get the common purpose achieved.”

China’s disregard for individual rights, equality and pluralism draws attention to America’s remarkable national success at sustaining all three. Some policy makers and intellectuals in Washington hope a “new Cold War” could unite Americans and revitalize the American creed.

As for Mr. Kennedy, he says the jury is still out on China’s ambitions. And he doesn’t think the U.S. can count on its Cold War model for national unity. “You can’t go home again,” he says, citing the famous Thomas Wolfe novel. Maintaining stable and inclusive politics amid unprecedented diversity is “not just going to happen automatically—you have to think hard about it and work at it.” That means recognizing that the U.S. has never been an ethnic state or a hodgepodge of groups, but a “national community” that stands for a distinctive creed, still worth aspiring to.

Jason Willick is an editorial page writer for the Wall Street Journal, where this article first appeared.