I have learned that it happens because BP2 and MBP2 replaces the default eye meshes with Elaborate Eyes meshes, and I can fix this problem by moving the eye meshes of BP2ed and MBP2ed into another folder and then redirect the paths in the corresponding .esm/.esp file. I'm pretty sure I also have to move the eyes texture of those two mods to another folder and then redirect the paths in the .esm/.esp files, correct?
Has someone already made it for him-/herself and would be so kind to share it? If not I'll try to fix it myself and then upload it here if I was successful, but then you might have to bear that I come back more often seeking assistance.