Modern America is a nation built and populated by immigrants, and the first wave of immigrants in the 15th century were more likely to be the ones doing the discriminating than the ones being discriminated against. Aside from the African slave trade, a lot of the early discrimination was against the indigenous population. For example, on page 255, the author states that immigrants coming into California during the Gold Rush forced "Indian men to work in mines and Indian women to work in their house holds."
The author states that the first true signs of discrimination against European immigrants occurred in the 19th century when America was starting to become an industrial force:
During the 1830s, however, the number of new immigrants rose to about 600,000, and in the 1850s, the figure skyrocketed to nearly 2.6 million. Nearly all these new arrivals settled in the North and West because the use of slave labor in the South offered few job opportunities in that region.
A lot of the new arrivals, particularly the Irish, were economic refugees, and thus angered the more established immigrants by working for less money and by working during strikes. If that wasn't bad enough, they were, along with the newly arrived Germans, mostly Catholic. In fact, the author states that it was the Catholic's fight against the country's Protestant ideals that lead to the formation of the anti-immigrant American Republican Party in 1843.