Well, I think that where we're at now is very different from most times in history. The economy is very different, and considering people were riding horses and buggies less than 100 years ago makes one pause when we use history as precedent.
We also have major problems with segregation and poverty in certain parts of our work force, and the poorest and least educated portions or our population are most affected by large influxes of poorly educated immigrants. This article/summary has some interesting data.
https://cis.org/node/4573
I do think that there is something behind Trump's popularity with the least educated people of our country, and it's not just bigotry and hate (although there's a ****load of this too). There seems to be a genuine fear and feeling of helplessness, and these types of people are particularly vulnerable to influence, as Hitler and Mussolini showed. Mass amounts of poorly educated immigrants affect the lives of these people without question, so I would appreciate a decision-making board to regulate immigration of the poorly skilled and poorly educated so that we can try to help the disenfranchised in our own country. I'm not saying only allow highly-skilled immigrants but rather not to allow millions of poorly educated immigrants each year, which could be a reality if we opened the boarders. If it turned out that every immigrant with a clear background who wanted to work in the US and pay taxes etc. was well within what experts found to be optimal, then, I would be all for it.
Europe's a whole other animal, and each country is complex and often very unique, take Greece, Switzerland, and Germany for example. The issues accompanying immigration are not complete by any means in Europe. I would argue that there is a difference between inter European immigration and extra European immigration. We will see how it plays itself out, but overall, I think the European Union has been good for the poorer countries and has streamlined many aspects of life within the countries of Europe in general.