As others have said, the Imperium is too vast to really answer "what is life like for the average citizen" with any reliability. I mean, if someone asked me what life was like for the average person on Earth I'd struggle to put together an accurate answer... not multiply that by near countless worlds, each differing in their environment and location. Life on a fortress world like Cadia
is going to be very different to that on a hive world like Necromunda
to a forge world like Antax
to one of countless other types of world.
If there was one general rule, it's that life is probably better the more isolated you are... not just from the other races but also from the Imperium. That's not to say that life will be good
but you're more likely to have a certain level of freedom and ability to develop your own life. Having contact with the other races is pretty self-evidently bad; their default position when it comes to humanity is pretty much kill/enslave them. They may kill them for different reasons using different methods but you're still dead at the end of the day.
Being under the Imperium's thumb doesn't necessarily make life much better. You're life is far more likely to be regimented with you assigned a duty from pretty much the moment you're born until you die without you really having much choice in the matter. Born in the aforementioned Cadia and want to be an artist or have pacifist tendencies? Bad luck... you're going to be a soldier. Born on a forge world and want to be a farmer? Bad luck... you're going to be an industrial worker. There are rare exceptions and the more privileged one's birth the more likely one is to escape being a miniscule cog in a vast machine... but you'll likely end up simply being a slightly bigger cog.
And political or religious freedom? Don't be silly. You even think of uttering a word (or sometimes even having a thought) against the Imperium or the Emperor and the best you can hope for is a quick death. Those Sister's of Battle you like? Their basic raison d'Ítre is to find "heretics" (ranging from actual heretics who may be a threat to political dissidents to people who simply had a moan about their living conditions) and burning them alive. And not just them. If you happen to live on a world where someone
started worshipping Chaos and put together a cult, chances are you're about six seconds away from the entire planet being nuked from orbit. Basically, the equivalent of someone killing everyone on earth because they viewed the Islamic State causing chaos in Iraq and Syria as trouble-makers and it wasn't worth the risk of just killing their forces and hoping it didn't happen again.
The 40K universe is pretty much the definition of grimdark
(the term actually came from 40K) for anyone involved.
The Imperium is basically defined by two concepts. The first is an unwinnable war combined with inevitable defeat. To take what is generally presented as its most serious threat, Chaos
, the Imperium cannot win
. It has no way of killing the Chaos Gods, of sealing them up, of preventing their forces from attacking or its own members from being corrupted by them. These are immortal creatures who will never stop; the best the Imperium can do is slow them down. All Imperial victories over Chaos are merely avoiding defeat and thwarting their plans and in time it is pretty much inevitable that Chaos will win... maybe billions of years from the in-game date but still, a victory. And that's just Chaos. There are lots of other races who would happily destroy the Imperium.
The second concept ties into the first and what was mentioned previously. Vast, vast, vast economies of scale. The Imperium is so big, with so many planets and so many people that a whole planet's population don't really matter, let alone individuals. Pretty much everyone is just a number on a scroll. That's why the Imperium will so readily kill billions of its own citizens; in a war they can never win it is better to kill a billion (a mere nothing to the Imperium) then allowing one traitor to live, however remote the chance that he actually achieves anything.
If you're under the Imperium's thumb you're not really an individual any more. You're a statistic. And no-one cares if a statistic is wiped out.