Alright, so anyone who has read the Horus Heresy novels knows that the great crusade was meant to bring the light of Scientific Reason, human dominance, and safety from the powers of Chaos to the galaxy. We all know that something went horribly wrong and we wound up with the current 40k universe with its dark gothic setting filled with religious fanaticism. An interesting point was brought up in the "So if the great crusade era marines are immortal now..." by Chainsworded Codpiece about the custodes being immortal and having seen the entire span of time covered by the imperium, including all the crazy that came after the crusade. This made me wonder why they haven't said anything. The only thing I can think of is that they have gone along with it because the Emperor wants them to. Here is why:

The Emperor's primary goal in life is to defeat the Gods of Chaos. This is what he was created for. During the era of the crusade, he did this by creating a secular human empire, where the gods were weakened by people's lack of faith and belief. Why did this work? The Dark Gods feed on the beliefs of humans and human-esque beings. If people don't believe in warp beings, warp beings don't exist.
However, without the Emperor telling people to believe in the light of science, people revert to religious belief (see the Lectitio Devinitatus). This belief in the Emperor seems to have the same effect on Warp entities though, as it is a direct contridiction of the Chaos Gods. The only problem is that if you believe the Emperor is a god then you believe in gods, which strengthens the ruinous powers.
The Emperor knew that the wounds done to him by Horus effectively ended his reign as a functional leader. He only had the ability to focus on the Astronomicon and such non-physical things. He could tell the high lords of terra to continue down the secular path, but that wouldn't work long-term. So what did he do? He knew about the lectitio divinitatus and encouraged it, because without someone ensuring that the Imperium was a place of science, he knew it would revert to a religious society anyway. The only "safe" religion was the one that worshipped him over the Chaos Gods.

This is why I believe the Custodes don't have a problem with the Imperium worshipping the Emperor.