Ill try my hand at explaining why motive matters sometimes and not other times.

Up this chain someone mentioned murder vs manslaughter. The difference between these crimes isn’t based on “why” someone did it. The difference is based on what level of “did you do this on purpose”. The various degrees of murder aren’t different based on the specifics of your justification. In the case of manslaughter the crime is usually “you were doing some generally stupid or bad thing that wasn’t murder and by bad luck you killed somebody “. Generally the “bad” behaviour in a manslaughter case did not have the goal of killing someone. That is very different than someone who planned out the murder of another person. If you plan out a murder because you hate that person for their race, believe murdering people will reduce climate change, or just dislike that person etc doesn’t have any bearing on the question of “ was this crime done on purpose rather than bad luck while doing some far milder bad thing”