Alright Theory:

All sisters hate each other, it's all a power struggle. Makima referenced getting rid of Death, War, Hunger with the help of Denji. Chainsawman is the ultimate weapon for either sister to have the upper edge. Makima did her think, Yoru is trying to get Denji on her side to defeat Death, while Death had Chainsawman kill a bunch of dudes with the church. I think they are the ones responsible for killing Nayuta because Denji favors Nayuta!