1968? Hmm...Nixon won there in 1968 and 1972. Ford won there in 1976. Reagan won there in 1980 and 1984. President Bush Sr. won there (albeit barely) in 1988. Since then, the GOP candidate has lost in California by large margins. So, the political problems there are much more recent than 1968, at least at the Presidential level.
Now, compare that with Texas. From 1968 to 2004, only one Democrat has won here -- Carter (barely) in 1976. Demographically, we have had the same growing Hispanic population as California. But politically, this state was Rat-infested at the state level. This began to change in the mid-1990s, and now Republicans run the state government at all levels.
The difference, I think, is that here in Texas, the GOP sees Hispanics as potential supporters. So, they work to earn their votes. In California, the state GOP sees Hispanics as enemies. Both states are heavily populated, with a large percentage of Hispanic voters. So, the GOP does well here and gets creamed in California. Well, duh!
Most surveys I've seen suggest that legal immigrants despise illegals.