Whether he was a racist himself is irrelevant.
"If the system is racist then he personally can’t be responsible because the system is responsible for managing him" - Maybe that made more sense in your head? Nazi soldiers were still Nazi's. To stick with the "few bad apples" thing I've heard people say - the actual saying is 'one bad apple can spoil the barrel'. If a rotten system resulted in a rotten cop, the cop is still rotten.
Isn't that what public defenders use? I don't know. Maybe in court dramas, but I doubt it gets much plan in actual courts. There are certain things used often in tv and movies such as the insanity defense that are seldom used in real life. Everyone I know who supports BLM believes this:
Justice should be equally applied. People are innocent until proven guilty and any time someone is deprived their day in court it is an injustice. It doesn't matter what George Floyd did or didn't do. Unless the police at the scene were reacting to an immediate threat, lethal force was not appropriate. So, to simplify, you can ignore George Floyd as irrelevant to the rest of this conversation. Derick Chauvin on video committed manslaughter and there was no immediate threat to warrant it. Floyd's past doesn't matter because that isn't the crime we are talking about. There should have been no hesitation in Chauvin's arrest for that crime, charges should have been filed, and he should have gotten a fair trial and his day in court.
I've never noted BLM marching to get charges dropped against someone or asked for special treatment. It has always been about seeking justice and accountability. I surmise that you listen to media that tells you differently. I welcome any actual evidence or statements issued by BLM that contradict what I'm saying.
I personally prefer not to get into motive, because it is (usually) unknowable. Often there are multiple motives and people aren't always conscious of all the strings that pull them. Was Chauvin motivated by racism? Was the initial effort to not charge him an example of systemic racism or just the system choosing to have a bad cops back over someone with a criminal record and race had nothing to do with it? Both are possible. I think in the end it doesn't matter. A bad cop killed a man, and people protested, marched, and (unfortunately) rioted over it. That's sort of the thing for me - even if BLM is wrong about motive, they weren't wrong about the crime and the near injustice.