Your map tells no such story. In particular, California's low rate cannot be attributed to California's policies, as California's rate is matched by Utah, Idaho, Texas, Mississippi, Alabama, etc.

You say Southern States have a higher death rate, yet Mississippi (typically considered archetypical of the deep south) a lower per-capita drug overdose rate.

Texas, which is a state dominated by the party that does not rule California has an overdose rate about 75% that of California.

There's a lot more going on than your analysis would suggest.