Conflicts are caused by many things, of course, and they are impossible to avoid completely; however, these three strategies may help avoid conflicts caused specifically by "disagreement and personal attacks."
First, assess the situation when it begins. Use your insight to reason rather than react, and do not automatically assume that the comment or attack is intended to be hurtful or cruel. Perhaps the remark (even if it is shouted in anger) is a desperate attempt to get you (or someone) to listen. Focusing on the person rather than the comment is likely to give you some valuable insight into avoiding a conflict.
Second, show empathy for the other person's point of view. We all need to be reminded that everyone has a story, and there are two sides to every story. Take the time to listen to a point of view which may be different than yours but which might also have some (or equal) validity.
Finally, find a way to compromise, even if it means agreeing to disagree. When people know that they are being listened to, they do not necessarily need to be agreed with; if you listen to others, especially when they are angry, they are more likely to listen reasonably to you.
If a personal attack or disagreement escalates into something potentially violent, it is usually best to avoid any kind of confrontation. Walk away if you are able. If, however, the situation seems to demonstrate some kind of control or restraint (and even loud disagreements are often manageable), these three steps will probably serve you well in preventing or avoiding conflict.