Those are all very abstract responses. What I mean is if you listen to the way the lore describes civilian life in W40K, particularly on Holy Terra, the imperium runs on a caste system. They don't call it a caste system and the specifics vary by world, but its clearly a caste system. Everyone is born into their role for life, with a few exceptions (usually involving military advancement, the death of a superior, or first officially joining the empire in some capacity).
The only "equality" in the system is that to anyone high up enough to warrant being transported in a spaceship, the landlubbers are so beneath their notice as to not count for anything. With the exception of the imperial guard. But yeah, ever serf has a job position they're born into and they could tell you exactly which serfs are higher up and which serfs are lower down. The hive worlds are the exception, with a Judge Dredd-esque breakdown of order due to population. But even then, being part of the system (AKA serving the imperial bureaucracy) puts you above everyone who isn't, even if you're cleaning the toilets.
Saying everyone in the imperium is equal is like saying "the people of westeros may kill each all the time, but at least everyone is an aristocrat." Sure... the POV characters.
There is a sort of equality among the higher ranks of the imperium... in the sense that the upper echelons of the bureaucracy are in a state of anarchy and collapsing in slow motion. Basically all imperial civil wars come down to two facts:
1. Within a given imperial hierarchy, be it the most glorious space marine chapter or the the administratium janitorium on backwaterius 9, orders filter down the chain of command with absolute authority. If your space marine commander tells you the imperial garrison on this planet are traitors, welp. Guess you're killing some guardsmen today.
2. Between the different branches, there is no concept of ranking AND there is no concept of absolute jurisdiction. Real life bureaucracies are designed so that for each problem there's only one agency responsible for solving it. The imperium on the other hand is designed to produce maximum overlap between the jurisdictions of both the different branches and the departments/military units within.
So yeah, a bunch of different ultra-powerful, armed to the teeth fanatics told that they can't directly give each other orders, given overlapping jurisdictions, and told that the final decider should they come into conflict is the "Emporer's will." I guess that's equality, from a certain perspective...