In his latest column here (Europeans Will Fight Back Against Invasion–No Matter What The NEW YORK TIMES Wants, December 22, 2016), Pat Buchanan wrote:

Liberals may admonish us that all races, creeds, cultures are equal, that anyone from any continent, country or civilization can come to the West and assimilate. That discrimination against one group of immigrants in favor of another—preferring, say, Lebanese Christians to Syrian Muslims—is illiberal and undemocratic.

But people don’t believe that. Europe and America have moved beyond the verities of 20th-century liberalism.

The cruel experiences of the recent past, and common sense, dictate that open borders are Eurail passes for Islamist terrorists, who are anxious to come and kill us in the West. We have to deal with the world as it is, not as we would wish it to be.

Specifically regarding whether promised assimilation will happen, we can guess that Buchanan himself is skeptical.  With good reason.  In the 1996 book The Case Against Immigration (free 1.4-MB PDF download here), NumbersUSA's executive director Roy Beck did some reporting from Wausau, Wisconsin, a small city in "America's Dairyland" that had been inundated during the 1980s and early 1990s with Hmong refugees, a legacy of the Vietnam War.  Here's part of what he wrote, with my emphasis added:

Any visitor to Wausau can observe stark lines of social, economic, and cultural differences between the native-born and the large—and largely poor—new Southeast Asian population. But a careful observer, says local history professor Jim Lorence, can look at who wields local power and at memberships in churches and other organizations and still see some faint signs of a continuing divide between the descendants of the Yankee settlers and of the Great Wave immigrants. Such signs remain even though it has been more than seventy years since the Great Wave ended. Americans contemplating the assimilation of the current thirty-year wave of immigrants might want to consider what America would be like today if Congress had not adjusted the gates on the immigration dam in 1924 and had not given the nation's diverse peoples forty years to adjust to each other without the constant large infusions of newer groups.

Other reporting from the same visit to Wausau appeared in Beck's classic The Ordeal of Immigration in Wausau (The Atlantic Monthly, April 1994), including this:

Various Wausau residents told me they favor a "cooling-off period" before more refugees are resettled in their city. Few residents know it, but such a period played a major role in creating the homogeneous Wausau they now consider the norm. After the turn of the century, immigration caused a social upheaval in Wausau. Back then the Germans and the Yankees were distinct ethnic groups, neither of which found particular strength in diversity. From 1880 to the start of the First World War, Germans streamed into Wausau, eventually overwhelming its New England Yankee founders. Jim Lorence, a local historian, says that the Germans became the predominant ethnic group around 1910. By the end of the decade the immigrants had turned the once conservative Republican town into a Socialist powerhouse. After the November, 1918, elections nearly every county office and both of the county's seats in the state assembly were filled by German-elected Socialists, Lorence says. Amid the political turmoil, natives felt like foreigners in their own home town. Around the nation this period was a time of sweatshops, worsening inner-city squalor, and ethnic hatred that propelled the Ku Klux Klan to its greatest popularity ever. The KKK, however, never got a strong foothold in Wausau, Lorence says.

Got that?  The "homogeneous" Wausau that greeted the Hmong refugees after Vietnam resulted less from earlier assimilation than from transformation.  Or perhaps even conquest.  And this had merely been due to the arrival of other "tribes" from Europe—other white people.

Even white Americans who move within the country can have difficulties.  That's one obvious conclusion from the Uncommon Knowledge series video interview, by the Hoover Institution's Peter Robinson, of J.D. Vance, author of the current memoir Hillbilly Elegy (which I haven't read).  Starting about seven minutes into the video, we learn about Vance's grandparents' move—for economic survival—from Jackson, Kentucky, in the heart of Appalachia, the 200 miles to Middletown, Ohio, in the Midwestern flatlands.  Then an exchange between the two :

Robinson: You state in Hillbilly Elegy that when they moved to middle-class Ohio, they did not behave like middle-class Ohioans.  They did not become suburban.

Vance: Yeah, that's right.  It took them awhile to really adapt to the cultural norms of midwestern, middle-class life.  One of the takeaways from the book is that culture is really sticky in a certain way.  You don't just all of a sudden acquire material comfort—and then all the habits, all the attitudes you grew up with, you completely cast off.

That's something my grandparents learned when they were integrating into 1950s nuclear-family, middle-class life in Ohio.  It's something I, of course, learned as an adult myself, that ... culture is sort of sticky.  So they did struggle to adjust in a certain way.

[Transcribed by PN, with emphasis as spoken]

Indeed, I recall, as an adolescent in a middle- to upper-middle-class Chicago neighborhood (in Rogers Park), being on the receiving end of such "immigrants" hailing from Appalachia.  The nearby large apartment building at the northeast corner of Greenview and Fargo, the "Birchmont," was an island of Appalachia in a sea of Midwestern respectability.

A story that made the rounds was of tenants in a third-floor apartment emptying bags of garbage out their window into the back "yard" below.  One time, several of us playing line-ball (softball) in the alley adjacent to the Birchmont were impressed into service by a just-arrived tenant: She pulled her car into the alley and insisted that we help tote her household goods—which included still-greasy frypans—up to her apartment.  And kids living in the Birchmont didn't mix well with us "native" denizens.

The Birchmont's filling-up with migrants from Appalachia was presumably an illustration of Center for Immigration Studies executive director Mark Krikorian's point (Immigration Doesn't Just Happen, National Review Online, April 18, 2011) that networks figure crucially in immigration dynamics:

No one wakes up one day in Rio and says to himself, “Today I will move to Weehawken!” People go where they have networks of relatives and friends and countrymen.

And then they may take their own sweet time assimilating.