I am reading an article by Numan Bartley called "The South and Sectionalism in American Politics," and one of his comments drew my attention:
Jim Crow segregation, like slavery before it, defined the social system in terms of color. Whether slaves or freedmen, the presence of large numbers of deprived workers, in addition to the general poverty of the region, discouraged immigration . . . the South remained old stock and Protestant, ethoculturally identifiable as blacks and whites, with that distinction written firmly into law and vaunted by the "White" and "Colored" signs that adorned the public facilities across the region."
Bartley says that the socioeconomic situation in the South during Jim Crow was not necessarily attractive to immigrants, but there are definitely examples of Latino/a immigration during this period, and some did stay in the South. So what was life like in Jim Crow south for ethnic minorities? Was it different from black southerners?
While I'm not a specialist in this area, my understanding is that Jim Crow laws targeted black Americans specifically. Other ethnic minorities were targeted de jure through other laws (i.e. The Chinese Exclusion Act) and de facto by virtue of white supremacy. The murkiness comes from how race was perceived and changed over time. In my specific area (Romani-American history) there are indeed reports of Roma being discriminated against under Jim Crow laws in the South. However, in these cases it seems to be more law and social attitudes creating a feedback loop--while JC laws were designed for African Americans specifically, they reinforced prejudice against people with darker skin tones/any who could be perceived as black/mixed. (And in these cases, some of the victims were indeed mixed race or were legally listed as "black" in census records).
Some of the laws covered under Jim Crow were also present in other laws specified toward other ethnic groups. Miscegenation ("race mixing," primarily targeting white/nonwhite couples) was illegal and enforced depending on the area and time. Initially it was specifically targeted toward Black and Native American men and white women, but began to cover East Asians, "Hindus" (both South Asian and Roma), and same-sex couples. Nayan Shah has a few books specifically looking at intimacy between South Asian men and other men.
Regarding Latino/as, depending on the time/place they were legally considered White. Socially they were still "non white" by comparison to Anglo Protestants, but blackness was almost always the defining mirror to Whiteness, so as long as you weren't "black" you could feasibly argue for a measure of legal whiteness. Syrians, South Asians, and ethnic groups we would consider "non-white" today were at times legally considered White. (See: White By Law by Ian Haney Lopez. Also again in my specialty, Roma could also legally be considered White, though there were American anti-gypsy laws that caused de jure discrimination.) There were other de jure laws, particularly in Texas, aimed at Mexican-Americans that mirrored Jim Crow.
The other things to keep in mind are demographics. There were indeed Chinese and Hispanic immigrants to the South as well as indigenous peoples, but de jure discrimination targeted these groups in different ways. Native Americans were not considered American citizens until 1924 (thus gaining the right to vote), though of course de facto discrimination and other legal issues continued well into the late 20th century (and into today, but that's not the topic at hand).
In sum: Jim Crow laws specifically targeted African Americans and people with any black ancestry, though who was considered "black" could be argued or manufactured. Other laws were in place that targeted other ethnic groups.