His record wont have any bearing on the case.
But it does in Public Opinion.
I wouldnt be so sure about that. Since Kyle is basing his case on a self-defense claim, the criminal backgrounds of his targets would seem to be absolutely relevant to the case. Establishing a pattern of violent behavior on their part would be essential to his defense.
There's a successful defense mounted on irresistible impulse.
After the trial, the judge compliments the defense on a successful prosecution.
The judge explains that to defend the shooter he had to show that the victim needed to die.
Here, we have to persuade the jury that the victim was the kind of guy who would do grievous harm or murder to the shooter.
So, yeah, his character is relevant.