My question is this; If Zimmerman or his bodyguard shot a member of the New Black Panther Party wouldn’t it automatically be self defense? They threatened him in a very public way, they are known to arm themselves and have a reputation for violence.
No. In order to justify the use of deadly force, one must reasonably be in fear of (apprehend) imminent serious injury or death. An alternative to having an actual apprehension of imminent serious personal injury or death is to repel a home invader. If you are female, "serious injury" includes unwanted contact of a sexual nature.
Zimmerman capping a New Blank Panther just because they are a$$holes is no more justified than Martin closing distance with Zimmerman in order to hit him.