Many of what are now of the 'poor white' class used to be a step or two above the economic/race class of those they considered below them. They had nothing to worry about in terms of competition. But due to primarily economic changes and perhaps demographics, they now find themselves on the same level or lower, and they resent it. During the upheaval of the 70's and 80's you mentioned, came much fear and insecurity. All of these factors led to a polarization of attitudes, and Trump represents, in part, a figure who can make sure America remains racist, while protecting those who feel threatened by people of color who have become more and more vocal about social injustice. When the 80's came, came the recession, and that's when the issue of the undocumented worker really heated up. They were seen as a threat to the white American pocketbook, and something must be done. Up until then, Mexican labor freely came across the border to serve our needs while we mostly looked the other way. Today, we have literally become hysterical about them. Even Blacks have picketed against them as a threat to 'their' security, which never was a problem in the past.
Some of it may have been related to economics as well as geopolitics. During the 60s, America was at a kind of economic peak, and many Americans were doing well overall. But Americans were also watching of the tumult on TV. While many felt safe from what was happening in Vietnam or the violence in the South or in the inner cities, they didn't like what was being done in their name and spoke out against it. Americans may have seen themselves as an invulnerable giant, yet still a bully that needed to be reined in. That's what the anti-war protests were about, as well as opposition to racism and other abuses of power within America.
But by the 70s, with the Arab oil embargo hitting us hard, and later on, with the Iranian hostage crisis - Americans started seeing themselves as more vulnerable and impotent in solving the problems we faced. Reagan and his ilk stepped up the Red Scare rhetoric and tried to make it appear that America was in serious danger - which led to Americans supporting more defense spending and stronger internal measures against crime (more police, more prisons, an escalated war on drugs, reduction in civil liberties, etc.).
In other words, it's easier to restrain ourselves when we feel like an invulnerable bully who can't be touched. But if we feel vulnerable and in peril, then we might be a bit more on guard and paranoid against outsiders.
One thing that should also be noted is that, in 1970, America had the lowest percentage of foreign-born population at any time in the 20th century (
https://www.census.gov/newsroom/pdf/cspan_fb_slides.pdf). Relations were slowly improving between blacks and whites, while immigrants were still a much smaller percentage of the population. Other ethnic groups had pretty much assimilated, but as a new wave of immigration hit, Americans started seeing an increased number of different language and cultural groups.
That may be where some of the pushback started. People who were generally okay with it in smaller doses may have felt overwhelmed, as if it was too much all at once.
Unfortunately, many coming across the border are now mules for the drug cartels, and so we have an exacerbated problem, which overshadows the issue of the need for viable work program for these laborers from the south. And so we pay rapt attention to the issue of the undocumented worker, rather than getting down to work on a creative plan to hire these much needed laborers.
A good deal of the demand for drugs comes from the US, which drives cartel activity along the border.
BTW, it was due to NAFTA that American corn growers dumped tons of cheap American corn onto the Mexican market, thereby putting scores of Mexican corn growers out of business, and driving their some 2 million now unemployed workers north to the US looking for work.
NAFTA was definitely problematic. It was fast-tracked and foisted on the people when they didn't even ask for it. It was also a complication that the elite were pushing for NAFTA at the same time they were pushing this war on drugs on the people. They would have been better off resolving the war on drugs one way or the other before passing NAFTA. You can't very well push for free trade and be anti-free trade at the same time.
Prior to the 70s and 80s, the actual percentage of undocumented workers was relatively low compared to later decades. I don't recall if there was any serious or severe need for labor during that time, although I think businesses were starting to react to the high cost of labor and the gains made by the labor movement in the post-WW2 era. It was clear that they were starting to look elsewhere for cheaper labor alternatives.
