If George Zimmerman had, hypothetically, a history of racially bigoted behavior would it be at all relevant to this trial?
Of course it would.
It would speak to Zimmerman's character, or really a lack thereof, and would inform the jury's perception of what kind of man Zimmerman is.
It might not indicate guilt in and of itself, but it might indicate the potential, or possibly a motivation, for commiting the crime he's been charged with.
Likewise, evidence that speaks to Trayvon Martin's personality and character is equally relevant.
This is especially true in light of the fact that the prosecution, the media, and the Martin family have waged a campaign of dishonestly since the night the shooting occured portraying Martin as some poor, innocent, child-like little boy, virtually the type of kid who would be afraid of his own shadow, when clearly he is anything but.
Now clearly nothing in Martin's history paints him as a hardened criminal, but when the defense's claim is that Martin instigated the fight that eventually led to his fatal shooting I think it's relevant that he quite demonstrably has a history of drug use, petty property crimes, behavior problems at school, physical altercations, gang participation (or at least giving the appearance of being a "gangsta"), and that he had recently been kicked out of his family home because of a pattern of unacceptable behavior.
