But: Obviously it is very important to change how to deal with people when a PersonalityConflict arises. Therefore changing an expectation here, a behaviour there, is the only way to make progress in this situation.
As a first step, people involved in personality conflicts need to understand that the problem only arises due to differing personalities. The problems people have are the same, the proposed solutions are similar -- there is no objective reason for a conflict in the first place.
The subjective PersonalityConflict can be alleviated when all people recognize.
The http://www.keirsey.com/ has a good personality test online. Take it. Read each others descriptions. Realize that those fundamental aspects of other people's personality will be very hard to change. Changing them is an uphill battle all the way. Don't do it.
Realize that other personalities are needed. A good trick used by team managers is to split people into groups where all have the same personality and ask them to solve problems. The Guardians will draw up rules, plan, control -- but won't get anything done. Artisans will imagine, show off, sparkle and shine -- and won't get anything done. Idealists will ponder the right way to do it, will discuss it, will work for themselves a bit -- and won't get anything done. Rationals will plan and invent grow bored -- they won't get anything done. Then the team manager rearranges teams such that the distribution is more even -- and suddenly there are people with the right ideas, people who actually do it, people who plan, people who test. Things get done. The downside is, obviously, that a certain level of PersonalityConflict is unavoidable.