I am a new convert to Catholicism. My parents are Protestants and are dumbfounded that I would have joined a Church with so much "false doctrine." My Mom established right from the beginning that she didn't want to talk about it because it makes her too uncomfortable/upset. But on our last visit home, we were talking about a kind Protestant man we all knew who recently passed away. My Mom piped up tersely, "I suppose you think he went to hell because the Council of Trent has so many anathemas against him." (not her exact words) My husband and I both said, "No," but then we were immediately interrupted by both the telephone and the children. We did not resurrect the issue after that, and neither did she.
If we had not been interrupted, I would have said that the reason the Church proclaims these anathemas is that it wants to protect it flock from heresy, as heresy is extremely dangerous. When someone willfully and deliberately becomes a heretic, they are cursed. But when someone believes something in ignorance, God may/does have mercy. But beyond that, I am not sure what I would have said.
Does anyone have any other good arguments or insights on explaining the anathemas to Protestants?