It’s pretty clear that a lot of the average American’s hostility to “illegal immigration” and “illegal immigrants” is, on a self-conscious level, driven by the “illegal” part. You’ll often hear people say that they love immigration, but they don’t understand why it can’t be done legally, the way grandpa didn’t it.
The reality that they don’t get is that your immigrant ancestors almost certainly came into the country under a very different border control regime than the one today’s unauthorized migrants face. Bryan Caplan notes the sign at Ellis Island, which says that only 2 percent of people were turned away there. Most Americans’ European ancestors came in during that period of de facto open borders. Meanwhile, there was no legal curb on immigration from Latin America until 1965, though there was a lot of quasi-legal harassment. But then anyone who came into the country from Latin America in the ensuing 20 years wound up getting an amnesty during the Reagan administration. Cuban Americans have been allowed to immigrate to this country without restriction during the intervening period, and of course the bulk of Americans’ African descendants came here on slave ships, not by getting an immigration visa.
You also have a fair number of people who get in under special visa programs for certain categories of high-skill workers. But if your family lore contains anything remotely resembling a classic immigrants’ story of a poor person coming to this country, and combining hard work with American opportunity to obtain a higher living standard than was possible in the Old Country the odds are overwhelming that this didn’t involve navigating anything resembling the current process by which a low-skill person can legally obtain permission to come here.