But there was no quota system (except from China-Japan-Asia) for any group till the 1920's.
That occurred at ports of entry, not on our land borders. In fact, the current configuration of our land borders didn't come into existence until February 14, 1912, when Arizona became the last of the 48 contiguous states to join the union. Oklahoma had joined in 1907, and New Mexico January 6, 1912.
No fencing or controlled entry points on our land borders with Canada and Mexico existed until recently in our history. So to repeat, our land borders have always been wide open and people have flowed freely across them in both directions throughout most of the time the U.S. has existed.
I say this not to excuse what has been happening over the last 20 years since President Reagan signed the first (and so far only) genuine amnesty for illegal immigrants in our history, but to explain it in part.