As a follow-up, is "Okie" the appropriate term to use when discussing this question or is it outdated? My knowledge of Dust Bowl refugees in California in the 1930s is primarily based off of Grapes of Wrath, so I apologize if this is an outdated term.
Depends on what you mean by cultural group. I don't think anyone calls themselves Okies these days. But many people who live in the Bakersfield region still speak with a different dialect and identify strongly with being from the South (insomuch as Oklahoma can be considered Southern). Many of these people are descended from the Okies, though it's a bit more complicated than that. So perhaps they never died out....
EDIT: look up pin pen merger in California
There was recently a BBC Documentary looking at the legacy of the grapes of wrath. I got the impression from the documentary that people were hostile at first, but began to understand the plight of the okies. The documentary is very interesting because it speaks to people who remember this period, and the pride they have for their families survival