(1) As the article points out -- in response to Jews fleeing oppression and Italians etc seeking economic opportunities -- the Congress passed racist quota restrictions and labeled them as "undesirables".
Under that policy, a mere 2% of the number of that group that was already in the country could gain entry. Thus, Jews for example who were in the country already at only a teeny less than 2 % of the overall population could barely get anyone in.
These policies on their face were based on race and ethnicity and had nothing to do with any of these immigrants' actual abilities, histories etc. It was simply -- "we don't want more Italians" and "no more Jews" etc.
During that time, it's important to remember that the KKK and it's supporters had many members in Congress and State legislatures - and they were pushing for these policies.
So -- let's not hold that up as a good thing. It was disgusting, and thousands died because of it, who would had they been let in been a great benefit to the USA society.
(2) with regard to your post. Today's immigrants for the most part do exactly what you say you miss --
they practice the faiths that are already here (tho not sure why that is an issue for you)- virtually 100% of the South American immigrants are Christians, and perhaps even more religious than many already here.
they learn the language at the same pace as the Ellis Island immigrants did. One generation. Those who work outside the home learn it faster, kids in school learn it the fastest of all, and home-makers or the elderly may never get a good handle on it. Same as with the European immigrants who came from non-English speaking countries.
And - they also love our country. They feel blessed to be here. They do not want to return to where they came from. They work hard, they raise their kids - indeed many of their kids end up serving in our military and putting their lives on the line to protect you and me.
I do agree with you that (outside of the hateful former quota rules) we should have the more liberal entry methods of the past described in the article, in which only an extremely small % of people were denied legal access, and people were given medical care right away etc. That would go a long way for getting more people to come through the legal process, rather than sneaking across the border.
Finally, I and most every Liberal that I know -- do support enforcement of our immigration laws and requirements. And although there are a tiny few who do push for "open border" concepts - that's actually only a very small group and mostly college age kids. It is not a Democratic agenda item and is actually opposed by most all Dems.
These issues on exactly what policy we should have on immigration and how best to enforce it are very worthy of discussion -- but let's not distort the issues as if they are between Trump's 5 billion dollar wall in the desert vs open border policy. Most sane and rational Americans -- including both Liberals and Conservatives -- are very much in between those two extremes.