I understand your point, but I believe three qualifications need to be made.
First, Muslim immigration is in an entirely different category from immigration in the 1800s and early 1900s from Northern Europe and from Southern or Eastern Europe, and immigration since the 1960s from Hispanic countries and from Asia. Muslim immigration carries problems unique to itself. In the past, most immigrants came to America because of its economic, political or religious freedoms (or all three together) and wanted to preserve those freedoms. We have never before had a significant group that didn't want those freedoms but instead viewed them as a threat, and intend to reject key Western values on which America was founded.
Second, while it's obvious we're having massive immigration in terms of raw numbers, I'd be interested in seeing numbers based on population percentages rather than raw numbers. Yes, we have more immigrants today, but there was a day when the United States had a far smaller population than it does today — the whole country had fewer people at the end of the Revolutionary War (3.9 million) than the combined population today of the New York City boroughs of Manhattan and Brooklyn — and I think the massive immigration of the 1800s may have been a significantly higher percentage of the population than what we're seeing today.
Third, there was a day when large parts of the rural Midwest spoke German, Dutch, or various other northern European languages of farmer immigrants, and large parts of our cities were filled not only with northern European immigrants but also impoverished ethnic ghettos where Italian, Yiddish, or various Eastern European languages were spoken and where much of the population was illiterate even in its native language and members of those immigrant groups went to work in horrible factory conditions. Our Hispanic immigration is following long-established patterns of immigration from Southern and Eastern Europe, filling bottom-of-the-barrel unskilled labor jobs that many Americans simply refuse to do, but in the process getting a bad reputation for a variety of social ills.
I don't see immigration as being a key problem in the United States. It **IS** a key problem in Europe, but the problem is that the immigrants are bringing fundamentally anti-Western values and European nations no longer have a shared Judeo-Christian ethic which teaches the value of work and personal discipline.
I'm not unaware of the problems of Hispanic immigration. I do believe in a Protestant work ethic, and that needs to be taught today to Hispanic immigrants for many of the same reasons it needed to be taught to Eastern and Southern Europeans in the 1800s. My ancestors were Italian, by the way, and phrases like “dirty Dago” and “wop” were once used the same way Americans today use “wetback” and “dirty Mexican.”
The bottom line, however, is that Europe's problems are multiple orders of magnitude worse because its immigration is coming from nations which are fundamentally hostile to Western culture in ways that Latin America is not.
Your ancestors entered the U.S. legally, which demonstrated respect for their new country's laws.