(1) Most Americans saw the Catholic Irish not as sharers of a common European culture, but as alien slaves of Popish superstition.
(2) Mexico, like America, is a European colony. Mexico, like America, is a Christian culture.
(3) Mexicans do see America as a land of opportunity.
They wanted to become assimilated and work hard to be productive and successful.
The Irish mainly wanted to eat. They never put out assimilation as an overarching goal: they built their own churches, their own schools, their own fraternal organizations, put together Fenian societies in the hope that prosperous American Irish would one day be able to launch an invasion of Ireland in order to break British rule, etc. "Assimilation" was not a articulatable goal for the Irish wave of immigrants. Eating regularly was.
It may have been language or various other cultural things. But they all wanted to adapt to American ways.
Incorrect. many had no desire to "adapt" to American ways, and refused to. To this day, Irish people in the US are obsessed with their Irishness to a bizarre degree. My mother's parents emigrated from the west of Ireland. I have cousins who support the IRA (even after 9/11!), who hate the English, who will only describe themselves as "Irish-Americans", not Americans, etc. St. Patrick's Day parades for them are tribal gatherings where they get drunk and extremely angry about perceived injustices to the Irish - even though they are all the sons and daughters of successful financial and legal professionals. When I tell them I'm not Irish, I'm an American, they get very upset.
They didn’t form a cultural underclass and expect our society to change for them.
They certainly formed an underclass and society did change for them - in good ways and in bad. The machine politics that cripple so many of our cities are in large part a legacy of the effect irish immigrants had on American culture and society.
Chinese and other Asians are good examples. Few immigrants faced greater difficulties than they. But they succeeded extremely well in becoming an asset to our nation.
And Mexicans will prove to be an incalculable shot in the arm as well.
I’m willing to argue that Irish immigration has not necessarily been an overall positive for the US. To this day, some Irish have a simmering resentment of Protestant Anglo-Saxons, the founding population of America. New York City was a self-governing and prospering city populated mostly by New England Yankees before the Irish landed in the 1840s and turned the city into a tribal fiefdom.
Most of the Irish came over after the potato famine of the 1840’s but I think you’re wrong in assuming they are so ethnocentric and “Irish first” as you seem to suggest. First, there are very few people of “pure” Irish descent except perhaps for some recent immigrants. That alone suggests they have assimilated into the American culture. The America you seem to describe sounds more like the balkanized Autro-Hungarian Empire. At best, the attitude you suggest is a very tiny minority in the USA of 300 million.