I think you're conflating naturalization/citizenship with immigration.
The Naturalization Act of 1790 (and subsequent) acts said you had to be white and have lived in the US for X years already to become a citizen. [1]
However, per your cited article a law was passed in 1882 to decrease Chinese immigration (who famously immigrated and helped build our railroads). [2] The Chinese immigrants couldn't become citizens but there was nothing (at the time) stopping them from moving and living and working in the US. [3]
Anecdotally and more recently: my Mexican grandmother, who married my World War 2 veteran grandfather in Mexico, legally immigrated just fine in the 1950s.
But, yes, most immigration was Europeans and African slaves but probably that was because it was expensive unless you effectively sold yourself. [4]
[1] https://en.wikipedia.org/wiki/Naturalization_Act_of_1790
[2] https://en.wikipedia.org/wiki/Chinese_Exclusion_Act
[3] https://en.wikipedia.org/wiki/19th-century_Chinese_immigrati...
[4] https://www.history.com/articles/u-s-immigration-before-1965...
> But, yes, most immigration was Europeans and African slaves but probably that was because it was expensive unless you effectively sold yourself.
You don't think it had anything to do with the Naturalization Act of 1790 that limited citizenship to whites, or the fact that even in 1965, congressmen felt the need to lie to the public and promise that law would not change US demographics? It was just because it was "expensive", that people from Europe immigrated, but not from South America?