So for example, if a Chinese or Punjabi farmer were to marry a Hispanic woman, or if a Japanese man were to marry a black woman, what potential consequences, if any, would these couples face?
The usual disclaimer is along these lines: These listings just indicate previous articles that may be applicable. This is not to discourage new questions.
A search for
jim crow asian
(merely as likely terms to have been in an article) includes a reply, When interracial marriages were illegal in some states in the U.S., what did biracial people do? Could they simply not marry anyone in those states?. They say they "assume" it was true in other states but provides no data, but they correctly note that Loving v. Virginia's Supreme Court decision says "While Virginia prohibits whites from marrying any nonwhite (subject to the exception for the descendants of Pocahontas), Negroes, Orientals, and any other racial class may intermarry without statutory interference." (here, in note 11).
I found a few more general posts, but they don't talk about marriage in particular, so I don't know whether they apply to marriage too.
How were non-black minorities treated in the Jim Crow South. /u/Dubstripsquads's reply says that different categories were variously treated as white or as non-white, depending on location or time.
There was also What was Jim Crow/segregation era America like for non-black minorities? It cites and approves of the book What Comes Naturally: Miscegenation Law and the Making of Race in America.
What was the status of Jews and Asians in America during racial segregation? is older and doesn't cite sources.