Goes to motive. If the prosecution doesn’t allege that Zimmerman was racist, that he had no business following Trayvon Martin or in any way portray Martin as squeaky clean and therefore incapable of attacking Zimmerman, the exclusion would be fair.
But if the prosecution alleges that Zimmerman was racist, Zimmerman has the right to demonstrate that his hunch was, in fact, correct.
If the prosecution alleges that in no way would Martin ever have been the type of kid to get in trouble, than Zimmerman has the right to establish that Martin was, in fact, a repeat criminal.
My understanding is that the prosecution, however, is based on those charges.
How so? The main question for a fair jury should be whether TM battered GZ without GZ having acted in unreasonable and/or unlawful fashion to provoke him. GZ is claiming that TM did exactly that. For a jury to accept GZ's version of events, it would have to accept that TM's actions were radically different from most people's normal actions. Much of the evidence the prosecution wants to exclude would tend to show that while the actions ascribed to TM aren't consistent with how most people behave, they are consistent with how TM used to behave. Such evidence would serve to corroborate GZ's description of events.