Consider the relationship between religion and conflict. Why can religion cause conflict?the crucible
Conflict, real conflict, generally only happens when people feel strongly about something--politics, religion, morality, life and death. If you don't feel strongly about something, for example, you're not too likely to risk much to defend it. Conversely, if you're passionate about something, you're more likely to risk everything to defend it.
Religion is a set of beliefs on which you can build your life--how to treat other people, what you're to spend your time and treasure on, and where you will spend eternity. When the stakes are that high, such as eternal reward in heaven or eternal damnation in hell, people are willing to fight drastic battles. Think Crusades and Gihad.
In The Crucible, these Puritans had very clear beliefs about what was and was not acceptable in this life and how sinful actions today would impact eternity for the transgressor. They had no mechanism for forgiveness of sins, so the best they could do was hide their sins from public scrutiny. No better way to do that than to keep all attention focused on the sins of others--shifting blame.
Abigail and the girls were doing what they shouldn't have been doing (sin); and, in an effort to avoid getting punished for their sin, they placed blame on others, innocent victims of the girls' sins. There's the conflict, and it was caused by the need to escape the consequences of sin as outlined by their religious beliefs.