History tells us "religion" or faith is the cause of most wars and conflicts around the globe; that's still true, at least to some extent, today. It seems to me the reason religion can cause such conflict is that every faith thinks it's right and must convert or eradicate others in order to fulfill the mission of that faith.
It's ironic that a religion of love and acceptance can create war and hate; however, true believers (plus the fanatic fringe of any faith) are motivated to win or convert others at any cost. Those who are not members of that faith can then become the "enemy."
When people are willing to die for a cause, unfortunately they're often willing to kill for that same cause. In The Crucible, the belief that witchcraft was a sign Satan's presence in their town caused them, in their religious fervor (and other motivations, as we know), to eradicate or "kill" any signs of this enemy of Christ.
I think Miller effectively argues that religion can cause conflict because of people's manipulation of it. Miller is quite skillful at being able to place the blame for Salem at the hands of the individuals in the position of power that did nothing to stop what was being done in the name of religion. They allowed the witchhunt to continue, permitted Abigail's lies, and encouraged public suspicion with a lack of collectivity because it solidified and consolidated their own power. It is Miller's genius to make the argument that religion, like politics, can be manipulated by those in the position of power over it and those who seek to gain other goals that are not sacred, in nature. I am not entirely certain that this is one brand of religion that intrinsically causes conflict. Miller's point might be that there can be perversion of the sacred in any context. The conflict that religion causes in the play is one rooted in misapplication and misuse in the name of advancing personal and political gain, as opposed to spiritual guidance.
To me, religion causes conflict because (by its very nature) it encourages people to think that their beliefs are the only correct beliefs. Because of this, it makes them intolerant. I think that we see this in this play.
In the play, the people of Salem believe very strongly in the idea that witches do exist and that people who act wrong are witches. Religion encourages them to think in this sort of dogmatic way. After all, religious beliefs are, by definition, given by God so there can be little rrom for compromise. Because of this, people who act wrong (like those who don't go to church enough or who oppose the minister's desire for golden candlesticks) aren't just different -- they are wrong and dangerous.
So I think that religion can cause conflict because it encourages people to think that their beliefs are God-given and therefore absolutely right. This makes them think that others' beliefs are not just different -- they are evil.