An interesting discussion...
Some points which have not been raised hower...
1. The Imperium as we are well aware is now so large so diverse and with so many different cultures comprising its mass, it has only one unifcating feature. The "Imperial Cult". What does a Space Marine of the Ultramarines have in common with a Atillian Rough Rider?
Common Language? Perhaps? Low and High Gothic appear to be the norm but on any world let alone a galaxy spanning Imperium different dialects and slang and cultural inflections would take hold. I doubt they would be able to communicate effectively without some problems. Look at our own planet... Germanic is the base for English, and its similiar in structure but that doesn't mean I could be walking in down town Berlin and understand everything. Across a galaxy the differences would be even more astute.
Common Cultre? No. The Ultramarine comes from a different world, a different value culture, to serve the Imperium and Primarch primarily, based loosely from a Romanesque style culture. The Atillian on the other hand is a nomadic tribesman, the idea of cities and a culture based off agriculture is foreign to him. Do they both value the city and what it stands for? Civilization? Merchantile expanse? The Ultramarine would... for the Rough Rider, probably not.
Common Religion? No. Its quite clear that the Imperial Cult is strongest in the standard human worlds which produce, protect, procreate all for the continuing needs of the Adminstratum, under the guise of the Emperor as a God. The Space Marine doesn't see the Emperor as a God, but as his progenitor of the primarch from which he is first loyal above all else. The Ultramarine worships the Emperor as a man, a fellow battle brother, the greatest among them who sacraficed himself for their future, he created the Marine who owes him his allegience. The Rough rider worships the Emperor due to the Imperial Cult... which states clearly the Emperor is a god and protects humanity from the evils of the universe and sacraficed himself so that humanity would survive. Although similiar they are fundamentally different in how they view the Emperor as a god or as a leader. If you ask the Rough Rider who he worships it is the Emperor... if you as the Ultramarine he venerates and respects the Emperor and his Primarch... for similiar but different reasons.
So how does a glaxy spanning Imperium hold these things together? Simply put they make the messages as simple as possible to communicate effectively. Its easier to destroy all psykers than to give certain strictures on their merits of if they can control themselves... A feral backworld on the edge of a sector with only a small Imperial presence would be lax if it allowed psykers to be confined and wait for a black ship that may take 1000 years to visit again, by then the world may be demon englufed. Their only viable option is sorry blow your head off. Mutation runs the same risk, especially if its allowed to run its course over centuries. Safer to destroy.
As an organization therefore to communicate across all these barriers of different cultures, the Imperium has little choice but to have one black and white rule... kill the psyker. Of course, then we have the exceptions, like the Primaris psyker, the pyskers of the guard, librarians and the Inquisition. But are they sitting there saying yes all pyskers are good? No. They realise the risk themselves, they are in fact almost the lucky ones of there deformity or evolution as they are allowed to exsist as they fill a needed role. But does a librarian even become Chapter Master? No. Does a Primaris Psyker ever lead a guard army to war and become a Lord Solar? No. Do Inquisitors? Yes, but only within certain guidelines... if they are fighting what? heresy which is usually demonic based in some form or against some chaos threat. The general rule of thumb is that the psyker must be killed as it endangers the rest of humanity to the perils of the warp and chaos.
As for the Imperial Cult itself... no doubt if the Emperor had been awake and able to direct the Imperium things would have taken a different course. But the simple ideas of black and white, good and bad, right and wrong... are what hold the Imperium together in his abscence of true leadership. Even if a primarch awoke or was re discovered, would he become the new Emperor or be able to command the Imperium in the Emperors name? Only Guilliman probably could and even then.... would the Space Wolves agree? would the Blood Angels agree? would the Black Templars suddenly reduce their numbers to conform to Codex Astrates rules? Would the high lords give up their power? Unlikely.
The simplest messages and black and white propaganda especially where psykers are concerned and the Imperial Cult itself are what bind the Imperium together. I don't think its hypocrisy.... I think its a matter or survival and giving motivation to the millions of different civilizations which make up the Imperium. Keeping one simple rule to bind them all together... Emperor protects against the "different" (psykers, chaos, tau, eldar, orks) and your role from humble peasant farmer to Imperial Governor is to stand with him and fight or rule or command or work. If you find the "different" destroy it before it destroys you. All of the Imperial Cults teaching reinforce this point... the Space Marine does it as its his duty but not because his god commands it.
Medieval Christianity supporting the Crusades (lets call it the Imperial Adminstratum and Cult) had the same thing going for it... Kill the different (Non Christian) as its coming to kill you... but you can work with the Byznatine Orthodox (Space Marines) as they are kind of the same... but don't allow yourself to fall victim to the different..