Closet Daredevil

his litany against Christianity in that same scene feels very personal, which could be for any number of reasons, but I think the line I mentioned in the previous bullet point is meant to provide context for it; he's expressing anger towards his mother and her loyalty to the church during her lifetime

similarly, when Blanc has his "road to Damascus" moment and his speech about giving grace to those who deserve it the least but need it the most, he's not really (or at least not only) talking about Martha; he's realized that he needs to find forgiveness and grace for his mother as well

Blanc's mother being dead would make him a thematic parallel to Monsignor Wicks, whose own unresolved trauma with his deceased mother informs his hyper-religious worldview (which stands in opposition to Blanc's hyper-rationalist one)

it also seems very intentional that when Father Jud prays for Louise, it's because her mother is dying and she doesn't want their last words exchanged to be in anger