What is the best way to communicate with others such that they will make strides to consider alternative viewpoints? I feel this would help to reduce anger in groups.
The only way to do this is through love. That is, propose a different perspective and a loving way. Be humble, show humility and respect others regardless of who they are. I learned this from the Bible, Jesus as the ultimate example. Love is not a feeling we have; it's a decision to treat people the way Jesus would treat them.
How to Win Friends and Influence People has some good ideas:
Emotional Intelligence can be something useful to study here as well.
Change or Die would be a book recommendation to consider if we are looking more at aiming at someone's behavior and the challenges associated with that. The book has multiple case studies that cover a lot of different areas including criminals, auto workers, and heart patients. There is a point about "Recasting one's story" that is similar to your remorse point though there can be the "acting as if" that may be done to get the reframing first that then leads to one wanting to make amends.
The Thomas-Kilmann Model would be a conflict resolution tool that may be useful to consider at times. Which resolution strategies do you use regularly? Which do you understand well enough to apply in various situations?