As one of the "sensible" conservatives on The New York Times' editorial page, Ross Douthat has a habit of using his column to provide a thin veneer of respectability to otherwise ugly ideas. Riffing off of the Cordoba House controversy, Douthat relies on the country's past experiences with unfamiliar immigrants to endorse nativism and xenophobia as a way of pushing immigrants toward greater assimilation.
But this is bad history; the nativists of 19th-century America weren't much interested in having "new arrivals adapt to Anglo-Saxon culture," rather, the nativists of mid-19th-century America wanted to keep immigrants off of American shores. [Just like now]