They don't now. Irish, Italian and East European immigrants were heavily discriminated against during the 19th and early 20th century. They weren't in fact considered similar. See these previous discussions:

• How did the Irish, Italians, and Jews become "white" in the United States?

• When and why did Irish, Poles, Italians, and other nominally white minorities get a race-lift to White?

• How much were Irish immigrants to the United States discriminated against?

Immigration laws didn't start with Hispanics. The first one was the Chinese Exclusion Act of 1882 and targeted (you guessed it) Chinese immigrants to the West Coast, as well as other Asian immigrants. See:

• In response to Obama's new immigration reform, some questions regarding the history of US immigration policy

As hilariously-usernamed /u/invisible_girlfriend points out, I don't think it's fair to say that the immigration law has ever "close[d] down the flood of immigrants." However, it's true that U.S. immigration laws have changed massively this century and especially in the last ten to twenty years. A recent criminal case decided by the New York Court of Appeals -- our highest state court -- sets out a good history of how deportations have spiked in recent years, with the main change being the removal of discretion from judges and the executive in deportation matters. See People v. Peque, 22 N.Y.3d 168 (2013). As that case explains, the consequence of this change has been felt most strongly by immigrants with criminal records. It used to be the case that a sentencing judge had discretion to recommend against deportation, and federal law enforcement would respect that determination, or lend significant weight to it. Instead, certain types of criminal conduct, and especially drug offenses, now carry pretty severe immigration consequences.

Peque goes back pretty far and comes up close to the present day. So some of this history violates the 20 year rule. Since we're already down the rabbit hole, another thing to look at is 1996's Anti-Terrorism and Effective Death Penalty Act. That's 19 years old so it's close!! The primary goal of the Act was to limit the circumstances in which a state criminal defendant can seek habeas corpus relief. It's had that effect, but the broader goal, of decreasing the number of habeas petitions, has not been realized in any way whatsoever. In fact, in the years since 1996, habeas petitions have spiked. It's impossible to say whether the same would have happened without AEDPA, or whether it would've been worse without the Act.

Limitations on habeas practice also affect immigrants. So AEDPA can be seen as part of a multi-decade trend of making it easier to deport undocumented immigrants, in any number of ways.

Whether that's stopped immigration... or resulted in the deportation of people the system actually want deported... well, I have strong opinions on the matter, but it's anecdotal based on my experience as a lawyer, and therefore beyond the scope of the sub. I'll leave you with a question: if immigration laws require more deportations, especially of drug offenders, and provide less discretion to the people executing the laws, but immigration officials have less resources to effect actual deportations, will the system necessarily catch the right guys, or just the convenient ones?

I'll try to go straight to the point here, since others have already touched on key issues. Two main factors have changed in the last 40 years.

1. The US economy. Instead of a huge country with plenty of both agricultural and industrial jobs for all, relatively well paid by international standards, both fields have seen their options shrink and decrease in quality. Instead we have systematically lost a great deal of industry and seen agriculture slowly taken over by huge corporate interests. Job opportunities are limited.

In response to this, US immigration policy has attempted to limit immigration so as to keep immigrants from 'takin' r jabs'. We grant limited visa quotas for unskilled labor so as to try to keep things on a relatively even keel. The idea being to allow enough immigrants to come in so as to take the really shitty jobs American's are unwilling to do for the pittance that companies are willing to pay, without affecting the well paid jobs that should be the backbone of the American middle class.

Keep in mind though, while we do have anti-immigrant policies in place and there is some xenophobia/racism involved (see point #2 below), this doesn't count for highly skilled labor. Even if you come from a country to which we grant very few immigrant visas, highly trained professionals, like doctors, physicists, chemists, architects, etc., have an almost unlimited supply of visas. Current immigration laws almost don't slow that flow down at all. But then again we are talking about an elite in the tens of thousands vs mass immigration by the hundreds of thousands or even low millions.

2. Xenophobia and racism. So called 'nativism' has long been an issue with immigrants. But as long as they assimilated and took their place in the hierarchy they were slowly accepted (WASPS, then Germans/Dutch/Scandinavians, then Southern Europeans, then Irish, etc). Underpinning American xenophobia since the 19th century are racist prejudices against peoples who 'wouldn't understand or be able to participate in Democracy' due to the history of their own country. Remember, Germanic, Hispanic, etc., were referred to and conceived of as races unto themselves up into the first half of the 20th century.

The Catholicism of Italians and the Irish was difficult for many WASPs to swallow, but they permitted it in the long run.

Mexicans and other people from Central America are dark skinned, however, triggering long held racial fears among certain sectors of the white population in the USA.

As such, pragmatic responses to changes in domestic issues (as discussed in point #1 above) can be and are compounded and mutated into tools of racism and xenophobia.

Part of the irony of people becoming so frightened of Mexican and Central American immigration is that US foreign policy played a huge role in the massive exodus from the region. NAFTA devastated huge swaths of the Mexican economy, particularly unskilled rural laborers. We supported dictatorships and oligarchies in Central America whose decades long civil wars against popular uprisings led to people fleeing the country as refugees. It isn't entirely our fault, but we should really be more self aware before we start criticizing immigrants for fleeing home countries whose disastrous conditions are partially the result of American meddling.