religion as a means of controlling mores and beliefs of the population would work.
the mirror universe is goofy. it can't work with billions of people murdering each other to become assistant manager of McMurderdonald's , there has to be some cohesion. A state cult of the Emperor, as someone pointed out makes sense. It could be where the Emperor exemplifies the state, or world of Terra, itself. This doesn't mean there isn't room for small state approved cults, polytheistic or otherwise, as long as they pay their taxes and don't oppose the current order.