I don't know about you, but if I was a perfect unchanging god, I would ensure that when I conveyed my message of perfect truth about my unchanging nature to my people, it would retain that state. I would make sure that no contradictions or mistruths arose in anything in the text. I would make sure my people understood the doctrines that I dictated to them. I would take measures to ensure that their beliefs remained in stasis.
However, this is not what we find when we examine the various religions of the world at all, in fact quite contrary to it. Tracing human history and the history of religion back as far as we can go is very interesting indeed. Along with culture and knowledge, beliefs and superstitions evolved as the ages went by. The first superstitious beliefs and practices were mostly comprised of rituals to try and cause the weather to change. This isn't particularly surprising as those early civilisations were very much at the mercy of mother nature. In fact today we are still at the mercy of the weather, just look at how much we get hurt when tsunami's hit, not to mention hurricanes and tornadoes too. Those early cultures did not have any of the knowledge we have today, or the ability to recover from disasters as much. A prolonged drought could force entire villages to choose between leaving their homeland and dying of starvation. In some places there was too much rain, and they would perform rituals to try make the rain go away.
For the most part, as culture and knowledge evolved magical superstitions and rituals declined in popularity per se. It is only honest to say that those prior beliefs and practices were at the very least misguided, and in all seriousness were simply wrong. They had misjudged the nature of the 'gods'. I find this similar in many respects to the decline of religious superstition. Until the advent of modern science, all functions of the natural world were typically attributed to gods, and religious belief and practices reflected this. Pagan cultures had various gods that were in control of each function of their environment. Sea gods, Storm gods, Love gods, War gods etc. Each step in the religious evolution of humanity was not necessarily developed out of previous belief as seems to be the case with the pagan religions. Monotheism seemed to have developed separately to polytheism, though the god concept itself must surely have had a common origin in ancient Mesopotamia.
Now does this view of the development of religion seem to reflect anything that would be postulated by an unchanging, omnipotent, perfect deity? Absolutely not in my mind. If you can think of a reason why human belief would evolve in such a way other than a simple heuristic desire to know more about the world around them.