"The real issue is which accent do Californians dislike most - a Southern accent or a New York accent?"
Speaking as a Californian with some early years in the Rocky Mountain states, I didn't like either type for quite awhile.
The typical stereotypes seemed to apply. The NY-Eastern types would be pushy big city folks. The Southern impression was of folks not too bright.
Many years in international business erased stereotypes. Sen. Sessions is one of the most consistently effective guys, when it comes to clear thinking and clear talking-accent or no accent.
And I had a boss from New Jersey, a stereotypical Italian guy. Smart as could be. Nice guy, too.
Something puzzles me. How do some people manage to not take on regional accents, or to shed same? Gingrich for example.
Gingrich was an army brat who lived everywhere. Still, my dad and his brother grew up in Brooklyn. My uncle had a quite strong New York accent, even though he moved to California in his mid-20's. My dad did not move to California until he was 40, and had almost no accent. I asked my dad why the difference. He said it was because he though the New York accent was ugly, and thus "never" spoke that way.