What would prompt one to change their worldview?
Since you have placed this in the Religion section, I will answer with regard to worldviews that involve religion.
One of the main reasons why people might change their worldviews has to do with things that happen to them. People might change their worldview away from a religious worldview if something particularly horrible happens. In such cases, people often question why God would allow the terrible thing to happen. This can change a worldview. By contrast, a person may have an experience that turns them toward a religious worldview. This can happen, for example, if someone has a great stroke of good fortune that they attribute to divine intervention.
In short, extremely traumatic experiences can lead to changes in worldview.