Fundamentally (no pun intended) the entire situation is summed up by "Which laws can preempt which laws." Specifically are God's laws superior or are the laws of men superior?

This question is the root of many violent clashes, especially where a smaller group disagrees on a preemption ordering than the larger group. In the US the most obvious example is the assertion that the constitutional rights of privacy between a woman and her doctor trump (or supercede) the rights of a group to declare abortion as murder. While many people will have different opinions on whether it is right or wrong to abort a pregnancy, when you read about bombing of abortion clinics or killing of doctors who have performed abortions, those perpetrators have stated that they believe they are enforcing God's laws above the laws of the land.

The narrative is that God's laws are more important because they determine if you go to hell or heaven, whereas the laws of men merely incarcerate you.

The challenge is that in the Medieval period people figured out that having laws under the control of a small group of people who were not checked by "the governed" gave rise to a conflict of interest which inevitably resulted in the law makers crafting advantages for themselves and their friends and to the detriment of the people.

As a culture it is important to respect and have tolerance for people who choose to follow their own laws, and it is essential to protect those who would choose not to be bound by a "cultural law" because they have come to disagree with that group. If you decide you want to leave the Catholic church because you feel their strictures on divorce or birth control do not align with your own values, then it is the responsibility of the society you live in to protect your ability to leave such an organization on your terms.

It is that last bit, letting people say "You know, I don't believe this is the right way to do things, I'm out of here." which is the essence of the rule of law having supremacy over the "laws" that a particular organization or group subscribe to. It makes those cultural laws voluntary rather than mandatory. And that undermines the authority of a religious figure to command your behavior and punish you for disobeying.

We call it Freedom of Religion but really it is Freedom from Religion. The right to choose to participate in a religious group, and to stop participating if you feel that is the right thing. Sure the group can excommunicate you but that is the limit of their "right" to retaliate, basically to not let you back into their organization.

There is nothing specific about this conflict of values. We have extremist Christian, extremist Jewish, and extremist Islamic groups. I would expect there are extremist Hindu and Buddhist groups as well although I don't know of any. But I do believe the battle here, both in the US with Christians and abroad with other religions, is about the idea that people should have the right to choose their own religion, and the right to choose no religion, and that the only laws which are mandatory to follow are the ones that we have arrived at collectively through a system where the government answers to the governed.