I'm no expert on this subject, but I can tell you that several cases cases did deal with this issue. Specifically Lum v. Rice comes to mind. This was a Supreme Court case that dealt with the issue of whether or not a Chinese-American, Martha Lum, could attend an all-white school instead of the colored school, and the court unanimously ruled that she was not entitled to attending the all-white school, and she could either attend a private school or the local colored school.

While not a SCOTUS case, in Mendez v. Westminster the 9th Circuit Court of Appeals ruled that California's school segregation of Mexican-Americans in the school system was unconstitutional in 1947, as California state law did not specifically legislate that the schools systems be segregated. After a cursory Google and FindLaw search, I found the opinion here. While this case does not indicate state-wide segregation of Mexican-Americans along the lines of Jim Crow laws (it actually does the exact opposite), it does show that segregation did at least occasionally apply to other races.

Someone else would have to tell you exactly how widespread this sort of segregation was, but I do hope this answer was helpful in answering your question.

Well, race is a social construct, after all. It wasn't something that could be applied across all of the United States. An excellent example is a book called The Great Arizona Orphan Abduction. In a nutshell, a group of Catholic Irish kids were adopted out to a bunch of Catholic Mexican families in Arizona. The Irish priests saw no problem with this, since in New York the Irish weren't treated as "white" anyway during this time. What was really important to them was that both groups were Catholic. However, once the kids got to Arizona there was a huge backlash among the local whites against the so called race mixing and the Mexicans were even accused of kidnapping "white" children. The point of this being that Americans' concept of race changed drastically depending on location and time period.

I know a guy whose father immigrated from China to one of the Deep South states (can't remember which) as a child. His widowed mother married an Irish American after moving here, and he adopted her children. I asked him this question regarding his father some years ago, and his answer was that since his father had a white stepfather, it was acceptable for him to use white facilities as long as he acted white. I raised an eyebrow at this point, and he said if his dad had had any hint of a Chinese accent, he'd have been in trouble. But since he picked up a good Southern drawl and mannerisms...he counted as white-enough.

So, by default he wasn't white. His step-dad made him conditionally white, provided he successfully played along.

I don't want to derail new discussion, as it's always welcome, But here are some links that have some good information!