There's also the possibility of a strong Asian-American influx. As I noted in a different thread recently, Hawaii saw major immigration in the late 19th and early 20th centuries because of a shortage of working population in its agricultural economy. While some of this included Portuguese and other European groups, the largest portion was Asian, which is why Hawaii has an Asian-American plurality in its population, rather than a white plurality. I could very well see the same thing occurring in California, particularly if it becomes oligarchically dominated by major businessmen, especially large-scale farmers who are likely to be hungry for cheap labor such as you might find in several East Asian countries at the time. Alternatively, if it stays with Mexico immigrants from China, Japan, and other Asian countries might with good justification be seen as more politically reliable and assimilable than Americans, causing Mexico to encourage or at least not bar the former while putting barriers to the latter, again tending to encourage an East Asian element in California. This would be particularly the case if there was some reason for the Mexican government to want to populate California, for example to build up a population base to resist American takeover. Mexico itself was somewhat underpopulated at the time, from what I recall, so it might want to reach out beyond itself for people to populate large, sparsely settled areas like California.
In essence, this would be an intensification of the OTL migration of Chinese (as well as Japanese, Koreans, etc.) to the state, amplified possibly by the more complex racial situation of an independent or Mexican California and perhaps, depending on the political structures of the state, by barriers to the construction of populist racist opposition to Asian migration that IOTL restricted Asian migration to the state severely in the late 19th and early 20th centuries. If we follow the Hawaii parallel a bit farther, encouraged by general Latin American ideas about "race mixing" and the fact that mixed-race marriages between Asians and whites have been comparatively less controversial in the United States than other types of matches, it's fairly plausible that the result could be a "new mestizo" triracial mixture of Mexicans, whites, and Asians forming the bulk of independent California's population, with Mexicans probably being the second largest group due to the constant intercourse across the state's border (as we see today with Tijuana). The same might be true of a California that remains with Mexico, too, although in that case you would probably expect, perhaps a bit counterintuitively, less intense contact between California and Mexico proper (i.e., no Tijuana, because there's no reason for someone to live south of the border and commute north--it's the same country, so they can just move)