Symbolism, Imagery, Allegory
Anthem has this mythic and ancient feel about it, and at times it even reads as if it were a work of scripture. A large part of that is because of the style in which it's written. (See "Writing Style" for more on this.) But it also helps that Rand makes use of a healthy amount religious language, and a few mythological and Biblical allusions.
The religious language isn't hard to find. In the very first sentence, we come across the word "sin" (1.1). Many of the other words used throughout the story to describe that which is forbidden in Equality 7-2521's society also have a religious resonance: Transgression, Evil Ones, Unspeakable Word, Unmentionable Times. It's often been noted that totalitarian societies adopt some of the trappings of organized religion, and effectively become religion for the population. Ayn Rand may be capturing that idea here.
But on the other hand, there's a noticeable absence of any positive religious words like "sacred," "divine" in circulation within Equality 7-2521's society. The only time Equality 7-2521 uses any such language while he is still in the City is when he describes the Transgressor as a Saint. It is once he leaves the City and discovers the word "I" that he starts to use positive religious language. And then it just doesn't stop: Spirit, temple, temple of spirit, sacred, and holy.
In the last chapters, there also seems to be a bit of mythic and religious allusion going on too. The most obvious case is the choice of new names by Equality 7-2521 and Liberty 5-3000 in the last chapter: they pick names from the Greek myths associated with gods of creation and (in Prometheus' case) light. But besides that, there are also a passages from Equality 7-2521's anthem to ego which sound a lot like verses from the New Testament of the Bible.
Check out, for instance, this passage on Equality 7-2521's three treasures:
I guard my treasures: my thought, my will, my freedom. And the greatest of these is freedom. (11.11)
This reminds us of a passage from Saint Paul on the three theological virtues:
And now these three remain: faith, hope, and love. But the greatest of these is love. (1 Corinthians 13: 13)
All of Equality 7-2521's proclamations about what he is – "I am the meaning…. I am the warrant and the sanction" (11.4) – also strike the ears rather like Jesus' famous "I am the way, and the truth, and the life" (John 14:6). The resemblance might not be precise enough to call these allusions per se, but at the very least Rand's language is similar enough to be suggestive of scripture.
All of this makes sense, given that Rand is trying to claim a special kind of sacredness for the human ego. Equality 7-2521's society has no understanding or appreciation of the sacred ego, and tries only to destroy it. It only draws on religious language to make prohibitions, because it only has the oppressive guilt element of religion down. Once Equality 7-2521 leaves his society behind, he is able to discover what is truly sacred for himself, and preach about it to us.