Given the context of the column, I think that Cohen is using "conventional views" to mean "culturally conservative views." But insofar as "conventional" means "based on or in accordance with what is generally done or believed," acceptance of interracial marriage is overwhelmingly conventional. A July poll from Gallup finds that 87 percent of Americans approve -- up from 4 percent in 1959.
The numbers don't vary much by region, or even all that much by age:
And note that the current president of the United States is the biracial child of a white woman married to a black man. America has come a long way.