Yes, other races were segregated. As an example I can use Seattle. The source I will be using is:

American Workers, Colonial Power: Philippine Seattle and the Transpacific West, 1919-1941 by Dorothy B. Fujita-Rony

Filipinos lived mostly in Chinatown during this time period. In fact, there is a bridge and park dedicated to/named after Jose Rizal near Chinatown (as an aside, it’s not really the case nowadays that Filipinos live mostly in Chinatown; the largest concentration in modern Seattle is probably in the south end and towards/in the Tukwila neighborhood). In Chinatown, migratory Filipinos lived in an area designated for people of color, white transients, and other “undesirables”.

Chinatown was very heterogeneous in terms of race/ethnicity: Filipinos, Chinese, African-Americans, undesirable whites, Native Americans, and Japanese all lived there. Jackson Street was around 70% Asian-American and nearly a quarter African-American.

Chinatown was a relative safe haven from the even more discriminatory and segregated parts of Seattle elsewhere. Filipino migrant Mariano Angeles remembered that they and other Asians were not allowed into the main part of a theatre, and were relegated to the balcony. Al Bautista said that Filipinos were not allowed into the main seating areas of a couple downtown movie theatres. “Relative safety” is a relative term though, and Filipinos and other minorities in Chinatown were still subject to abuse. Filipinos were assaulted or killed by police officers, and were regularly thrown in jail for dating or being around white women.

Anyways, this is a short write-up, but from this I think you can get an idea that, yes, segregation was absolutely enforced on other non-white groups.