You are a
It's in your best interest to just leave me be
This is the best policy when you have one.
Alone I protect and work when I shouldn't
A scab protects an injury while it heals. It also means a strikebreaker.
If I get mixed up with you I'll take a dive
Squeeze in a sun god the wrong way and I will bug you
SC(AR)AB. It didn't need to be the wrong way: SCA(RA)B.
Decapitate me if you have places to be
Cut off my tail to hear the sounds of Jamaica
SCA. (Usual spelling is SKA, but it is "to hear" ...)
Do both and I'll just be a bear
Perhaps because of the identification of California (CA) with the grizzly bear.