Past crimes are almost never allowed as evidence. Because they aren’t. In this instance his killers had no way of knowing his rap sheet, and he had no stolen property on him.
The evidentiary admission question is - does its probative value outweigh any prejudicial effect. Prior bad acts may be relevant and admissible as evidence, or not.
The father and son were renovating houses. There were several break ins reported for mostly copper wire being stolen. They saw Aubrey trespassing illegally in construction areas. (Obviously a fan of sh!t box 1960’s architecture) They placed him under citizens arrest. He resisted, assaulted the father and tried to grab a shotgun away from the son. According to Georgia’s Stand Your Ground law, citizens can use deadly force to defend themselves, other people, or property if they believe such force is necessary to prevent death, bodily injury, or a felony. The father was assaulted. Aubrey has his hands on a shotgun barrel and is trying to wrestle a shotgun aimed at him. He was lawfully placed under Citizens arrest for illegal trespassing. It was a legal shooting. Again just caved to wok mob.
The elder McMichael was involved in Arbery's case in which he brought a loaded gun to a school event, so yeah, the former police officer *DID* have a way of knowing his rap sheet.
He was an investigator for the District Attorney's office. It doesn't get much better than that in knowing all the local criminals.