After using the "magical axe of undoing" I unchecked the ESP and BSA of the mod, removed them from the Data folder, and tried to load Skyrim. It CTD'd immediately (before loading any saves).
If I return the ESP and BSA to the Data folder, even without checking them, Skyrim loads. And even if the mod is not checked, the assets from it still appear in the game.
I checked my Scripts and SKSE folders, there is nothing in them that belongs to the mod (and I always used the BSA version of it anyway).
What could make this happen?