I do not think that "becoming American is the same as becoming a WASP". What I think is that the core group defining USA as a culture are Protestants especially of British background. Yet the people of different religious and ethnic origins can integrate with the American society to the degree that their cultural mindset is compatible.
German and Scandinavian Lutherans were integrated rather smoothly with British Calvinists (Congregationalists and Presbyterians), so were the Episcopalians/Anglicans (despite their loyalist leanings), various more home grown groups like Baptists or Pentecostals are in sync by definition.
Integration of Catholics was a difficult process, but somehow went OK at the price of redefining aspects of American culture (Orthodox could find a place in opening created by Catholics).
Harder to integrate were Mormons despite of their domestic origin.
The real question is if Muslims can be integrated in large numbers. Or if the large influx of Latin Americans with a very strong identity will not prevail over British element. If they do, USA will become other Latin American countries.
Buddhist/Confuctionsts tend to conform and to convert. Hindu so long as they adhere to the cast tradition can remain within their own circles avoiding conflict, as they change they will be more willing to adjust or even convert.
The last but not the least the militant secularists cannot fit by definition, but they abort/gay themselves out of existence.
When you think about the word "integrate" do you consider "merge" or "sustainable society" to be a synonym? IMO The sustainability of humanity is proportional to its diversity of culture and ideas. Cognitive clarity of the - past * present * future - is something that many minds asymptotically approach together. That's the real power of the United States! The philosophical and cultural contributions to our society do come from the Protestant Reformation but what do those ideas actually do for us? How did those ideas transform into Super Power?
The power of Reformation logic is that it makes room for diversity of culture and ideas. Do not give it uni-polar credit for creating new culture and new ideas. Agreeing to disagree opens the doors blocking progress and prosperity for all mankind. Now let's ask the question again, why are we powerful? Americans manage to live through iterative bouts of disagreements, learning from each, and finding new agreements about the mechanics of humanity. The more we know about us, the more able we are to face unpredictable challenges to us. In America, us, can fit any human being you can imagine.
In this work, Huntington has utterly missed the point. Why? I think he's an antisocial sociologist. Somebody needs to remind him that humans are the most social entities on the planet. Between you, me and Huntington, let's make the point clear. WASP logic facilitates society but is not directly responsible for it. WE ARE!