A widely accepted way of thinking or behaving is a convention.
It denotes set of generally accepted standards and norms and a way in which something is usually done. Example for convention is shaking hands when greeting someone. Controversial on the other hand is something causing people to have opposing ways.
She could not believe that such a violent (or vile) act would be committed.
I am pretty sure that description above belongs to Nancy Lammeter. I choose this option because, as far as I remember, both Silas Marner and Dunstan Cass are morally-weakers. What about Godfrey Cass - he is just opposite to Dunstan which does not concides with the description. I think it's clear, regards!