Circumstantial and constitutive moral luck are the ones that bother me the most.
With circumstantial, the person might not have done something blameworthy if only they hadn't been in the wrong place, with the wrong person, etc. What that seems
to imply to me is that if someone forced someone else into a position where it is way more difficult than usual not to do harm, the former was able to take another person's potential for morality away from them against their will. Kind of disturbing to me, as a person who wants to do good, if that's a valid interpretation.
Constitutive moral luck is when a person was shaped by their environment or their mental condition. What bugs me about that is how it can be taken to mean that people can be born with a moral handicap. If they're born into an environment that promotes selfishness, and it's a difficult environment to get out of, the struggle will be greater to resist the influence. If their genes give them a mental disadvantage that makes it easier to abuse other people, did their genes also give them a moral disadvantage?
A message that could be taken from both is that it is not just a personal but a moral imperative to improve ourselves upon what we were born with and to learn to spot and strengthen ourselves against circumstances in which we could be manipulated into immorality, because doing so can indirectly prevent us from doing wrong.
I'm hoping that I misinterpreted most of the above.