In many ways, Latino, Asian and Native Americans faced the same kinds of discrimination that African-Americans faced during the Jim Crow period. Native, Asian and Latino Americans were even lynched in the same way African-Americans were (though certainly in smaller numbers). Segregated schooling for Latino, Native and Asian Americans existed and had the same issues as that of African-Americans ie. extremely limited funding and limited secondary schooling. California even differentiated between children of Japanese, Chinese, and Mongolian descent.

This 1971 Campaign flyer for Victoria DeLee, a prominent South Carolinian Civil Rights leader, gives interesting evidence regarding Indian schooling in South Carolina. " [she] waged a successful battle to enroll American Indian children in the regular schools of Dorchester County." Native Americans also faced problems with the Ku Klux Klan as evidenced by the 1958 "Battle of Hayes Pond" in which Klansmen staging a rally against Native Americans in North Carolina were outnumbered and attacked by Lumbee Indians who beat the hell out of the Klansmen and drove them into the swamps.

Two cases that might interest you would be Mendez v. Westminster (1947) in which the Ninth Circuit Court ruled that segregated schooling for Mexicans and Mexican-Americans was unconstitutional, and Hernandez v. Texas (1954) decided by SCOTUS ruled that all groups (Not just White Americans) benefited from the 14th Amendment.

In regards to books you should look at:

Lumbee Indians in the Jim Crow South by Melinda Maynor Lowery. Lowery gives an excellent overview of the situation the Lumbee lived in during the Jim Crow period and how this racial "other" organized and thrived.

Fighting their Own Battles: Mexican Americans, African Americans and the Struggle for Civil Rights in Texas by Brian D. Behnken. A fantastic overview of the Mexican American Civil Rights Movement in Texas which gives some fairly in-depth accounts of how Latino schooling and social life worked.

James Loewen's book "Mississippi Chinese" (1971) addresses this question as it relates to Chinese immigrants in the Mississippi Delta during the latter years of formal segregation. When they arrived, these immigrants were mostly seen as neither black nor white. However, since they were a mostly poor demographic that worked menial jobs (mostly owning groceries, as I remember), they started out being seen as "closer" to black. Over time, though, their liminal status actually gave them more upward mobility - especially as their businesses prospered, marriage, etc. Their increased prosperity led to them gradually being more accepted by the white community and eventually seen as being "closer" to white than black. The book also explores how the Chinese immigrants had largely never experienced racial discrimination before (in China), but only class discrimination. Loewen concludes that it was their ability to change their class status that allowed them to also change their social status.

Follow-up: particularly in the South, where Jim Crow laws officially enforced segregation. Would a Chinese-American be considered "colored", white or something else?

I took a justice and law class in college that talked about Yik Wo vs Hopkins. This case happened in 1880. Basically, a guy running a laundry service in San Francisco didn't have a permit and got jailed by the sheriff. The case went all the way to the Supreme Court and tested the validity of the 14th Amendment.

Basically, the Supreme Court actually ruled in favor of the Chinese plaintiffs, saying that

The rights of the petitioners, as affected by the proceedings of which they complain, are not less because they are aliens and subjects of the Emperor of China. By the third article of the treaty between this Government and that of China, concluded November 17, 1880, 22 Stat. 827, it is stipulated:

If Chinese laborers, or Chinese of any other class, now either permanently or temporarily residing in the territory of the United States, meet with ill treatment at the hands of any other persons, [p369] the Government of the United States will exert all its powers to devise measures for their protection, and to secure to them the same rights, privileges, immunities and exemptions as may be enjoyed by the citizens or subjects of the most favored nation, and to which they are entitled by treaty.

The Fourteenth Amendment to the Constitution is not confined to the protection of citizens. It says:

Nor shall any State deprive any person of life, liberty, or property without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

These provisions are universal in their application to all persons within the territorial jurisdiction, without regard to any differences of race, of color, or of nationality, and the equal protection of the laws is a pledge of the protection of equal laws. It is accordingly enacted by § 1977 of the Revised Statutes, that all persons within the jurisdiction of the United States shall have the same right in every State and Territory to make and enforce contracts, to sue, be parties, give evidence, and to the full and equal benefit of all laws and proceedings for the security of persons and property as is enjoyed by white citizens and shall be subject to like punishment, pains, penalties, taxes, licenses, and exactions of every kind, and to no other.

The full court opinions are here.

Knowing how the Civil Rights movement wouldn't happen for another 80 years or so, I was so surprised then and still surprised now that this case ended up with the Court unanimously upholding the Constitutional right of a person of color.

On my phone right now so can't link sources but Hispanics in the US were counted as whites until the 1972 (off the top of my head, I know it was 70s) census