The answer is "yes." I am going to come at this from a legal history perspective (and one that focuses primarily on Chicanos (Mexican-Americans)), but I am sure that someone else here will be able to offer a different perspective.

Just a couple of months before Brown was decided, the Court considered the case of Hernandez v. Texas. In this case, Chicanos were being excluded from juries. Over 25 years, not a single person with a Chicano last name was picked to serve on a jury. Before Hernandez you had to be part of what's called a "suspect class" in legal terminology, which refers to a very small select groups that can't be discriminated against without really good reasons. Of these classes, race is probably the most well-known.

Before Hernandez, lawyers for Chicano plaintiffs sometimes employed the "Other White" legal strategy. This strategy involved claiming that the Chicano plaintiffs were actually white, and so could not be subjected to discriminatory legislation aimed at blacks. As you might imagine, this strategy doesn't work in Hernandez. The Texas courts simply said "Mexican-Americans are white, and all the members of the jury are white, so there isn't any racial discrimination." The lawyers in Hernandez appealed this and argued that while Chicanos may actually be white, that doesn't matter because they're being treated as a separate class from white folks. The Supreme Court agrees and issues a fascinating ruling that if a group of people are treated as a separate class, they can qualify for protection under the 14th Amendment. The Court found the long history of discrimination against Chicanos in this county dispositive in determining that they were a separate class from whites. Examples of this discrimination included separate toilets for whites and Chicanos, school segregation, and a sign that stated no Mexicans would be served at a restaurant.

Now before Hernandez, we also see some other examples of discrimination against Chicanos and other other groups. Mendez v. Westminster is a 1947 (so seven years before Brown) federal case that ends up only going up the 9th Circuit. Here, Chicano plaintiffs were challenging the segregation Mexican-Americans into separate schools. I think it's important to note that Thurgood Marshall, who later argued Brown for the plaintiffs before the Supreme Court, wrote an amicus brief for Mendez. Ultimately the Court ends up ruling that this kind of segregation in this specific instance was unconstitutional. After Mendez the legislature repealed sections 8003 and 8004 of the education code, which until their repeal had legalized school segregation for Asians. Lopez v. Seccombe further illustrates this. In this case, San Bernadino was excluding Chicanos, Puerto Ricans, and other persons of "Latin descent" from using a public park and playground and its facilities. There, the court found that this segregation violated equal protection clause.

All of this shows that other groups were discriminated against during the Civil Rights Era. They faced some similar forms of discrimination (such as school segregation and lynching), but they also faced their own unique kinds of discrimination. So as not to give you too shallow an answer on that, I will leave that to folks with more specific expertise.

Sources:

• Richard Delgado, Juan F. Perea, and Jean Stefancic, Latinos and the Law.
• Juan F. Perea, The Black/White Binary Paradigm of Race: The "Normal Science" of American Racial Thought, 85 Cal. L. Rev. 1213 (1997); 10 La Raza L.J. 127 (1998).
• Ian Haney-Lopez, Race and Colorblindness after Hernandez and Brown, 25 Chicano-Latino L. Rev. 61 (2005)

Cases:

• Hernandez v. Texas, 347 U.S. 475 (1954).
• Lopez v. Seccombe, 71 F. Supp. 769 (S.D. Cal. 1944).
• Westminster School Dist. of Orange County v. Mendez, 161 F.2d 774 (9th Cir. 1947).