If Martin was the one who was on trial, then I could see the exclusion of character evidence. In a trial, the prosecution cannot introduce evidence of bad character unless the defence first introduces evidence of alleged good character. But Martin is not on trial. What the court needs to determine is if Zimmerman is telling the truth. Was Martin a bad ass who had no lawful purpose being in that neighbourhood or an innocent person just strolling along minding his own business? Was he an angel or someone who had previously engaged in unlawful behaviour? This evidence would help bolster the authenticity of Zimmerman’s recollection. It should be introduced and the refusal of the judge to permit it could result in any conviction being overturned on appeal.
I agree with your remarks and conclusion. Evidence that Miami authorities suspected Martin of burglary is relevant to the claim that Zimmerman wrongly profiled Martin.
On your blockquote, and I'm sure you know this, but there are other possibilities. Martin could have both lawful purpose (going to a home where he is a guest) and unlawful purpose (case or burglarize) at the same time.
I'm merely speculating that Nelson will exclude the evidence, and she'll misinterpret the law to obtain that outcome. She's protecting the state.