For the notion of absolute not to exist would be an absolute absence, a requirement that everything lack this kind of perfection. This, of course, would contradict the absolute absence of perfect absoluteness. At least one thing would be absolutely required -- that no rule be absolute.
That may strike you as a word-game, but it is not. Logic depends very strongly on principles that are intuitively absolute. Contradiction is possible only if the truth of certain kinds of propositions is absolute. Otherwise, carefully cultivated, the tiny risk that all the things we find contradictory actually admit exceptions slowly add up to a basic incapacity to process the world (or an enlightened state of non-dualism that breaks one's obsession with trying to process the world -- Samsara is Nirvana -- same thing, different day).
Arithmetic works only if equality is absolute, as does the rest of mathematics. Even our science's understanding of the lack of absoluteness, in statistics, requires a notion of 'real randomness' -- an absolute lack of predictable order -- in order to become tractable. We could go on, but in fact, the notion of absoluteness is almost everywhere.
Whether that notion has any basis in actual experience, or in physical reality is another question entirely. But, as the list of examples in the paragraph above could go on for quite some time, it is clear that our internal experience is shaped very strongly by a search for absoluteness, and an ultimate compromise with the inability to find it.
(Like the philosophy of mathematics, I think the best approach to the philosophy of religion is upward through psychology. So the rest of this answer is from various psychoanalytic perspectives that many people put outside the boundary of philosophy proper, and surely outside of theology.)
From a Lacanian point of view, it is the imagination that is absolute. A human has only a limited capacity of attention, and what is missing from any internalized image is missing absolutely. Firm boundaries are drawn around each imaginary object. (Even if those boundaries are 'drawn in fuzziness' like the fake fur on CGI animals, or inked with the 'non-color', we kind of live in cartoons.)
But from that perspective, the ability to symbolize, and thus to communicate, depends entirely upon using current reality to create scenarios in another person's imagination. You can point at a rock, and claim you have communicated without invoking imagination, but there is an imaginary signification of that rock as special. You have 'named' it, personified it a little bit, and you are telling a story about it.
Giving up entirely on idealism and absolute statements always fails (Buddhist miracles notwithstanding), even if you consider it entirely hopeless, because idealization is the bedrock of our basic concepts of language. Since language is what we will use to capture a rule, every rule is implicitly absolute, even if it says otherwise. It is also therefore just wrong in some unforeseen way. (Ask any three-year-old, wait a bit, and ask her again at nine.) We know that is not real, but it is our natural framing. Even the resulting relativism is expressed in terms of purposive refusal to choose a preference, rather than having some normal, positive expression.
That is why, going back to Lacan, the natural human mental state is slightly neurotic. Following on that, it is also why we have a major personality trait among the "Big 5" for resentment and distrust (Neurotic), while all the other major personality components admit positive characterizations (Open, Conscientious, Agreeable, Engaging).
Going back to the God question, this is why, from a Jungian point of view, religion is mandatory in human psychology. If you displace your religious inclination purposely from a given fixed perfection, you still must choose an object of baseless faith, be that human potential, scientific process, or the nature of suffering. Your dependence upon that new fixed object will be just as absolute a religion as the one handed down to you -- though it may make more sense in your context, and it may change daily. Because that is not really a change, either: Religious people's religion is also coped to their context, and whether they like it or not, it also changes daily.