What rights do citizens have in theocracy?

Not many. As we know a theocracy is defined as a government set up, in which god/deity is the surpereme ruler. it's Rules and customs are based on the particular religion. So for example, if the United States were a theocracy, it would be Mandatory to go to church on Sundays. It would be illegal to believe in other gods. You have no rights. The only right you have, is what preached by the church.