A Democratic Theocracy is a form of government that enforces religious law depending on someone's religion. For example, if someone is Muslim, they follow Shari'ah. If they're Christian, they'll follow Biblical Law. If they're Jewish, they follow Jewish law. The same goes for other recognized religions in El-Amin Caliphate (which always get promoted or demoted to or from recognition).
What if one religious person commits a crime against a person of a different religion?
There are multi-religious courts that accommodate tricky situations like this. If the offender is found guilty, he or she would be sentenced according to the religion the criminal practices.
In the case of how a court hearing proceeds, that will also be according to both parties' religions. For example, in Al-Islam, the parties should invite 4 witness (correct me if I'm wrong in the form of a Telegram Muslims). This also goes for Christians, Jews, etc., according to what their religion says.
What about Athiests and Agnostics?
Atheists, Agnostics and God-conscious people who don't adhere to a religion will follow the usual laws EC's democracy upholds.