Sorry, but if you think becoming American is the same as becoming a WASP, there's really nothing more to say. This nonsense popped up with the Know-Nothings (the modern heirs of whom seem to populate FR), was disproved then and shown to be the mere bigotry it was, and I think the modern anti-Hispanic hysteria will meet the same fate.
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.