Tolkien admitted that Christianity influenced themes of Lord of the Rings, even while he disparaged the blatant allegory of C.S. Lewis. Like Satan, Sauron is a corrupted angelic being, and the personification of evil. Though for the characters in the story most of his deeds are done through his agents, he is also a literal person who rules over a very real place. Frodo's descent into Mordor is an intentional echo of the mythical journey to the underworld, the Hero Cycle's symbolic death. But the conflict between good and evil in the Lord of the Rings does not simply come from battling Sauron's orcs, Ringwraiths and other minions, but from battling against the corruption of one's heart. In a universe where objective morality exists, evil is committed by willfully siding the the Enemy of good. The Christian notion of temptation requires socially agreed upon sins, so that when transgressions occur, it is obvious to the one who commits them. We can look at Boromir, who at the end of the novel succumbs to the temptation of power and attempts to acquire the ring for himself, but he knows full well that the ring cannot offer him the power to protect his homeland only a temporary blindness confuses him, and when it passes he acknowledges his sin and repents. But when evil can be identified, it can also be overcome. It gives us the option of choosing righteousness and bettering ourselves as individuals.
As a secular person myself, I'm not trying to claim that either Tolkien or Martin have a superior moral worldview, but am just trying to observe them from a cultural historical perspective. It is interesting that Tolkien, who survived WWI, by all accounts a nebulous and ultimately pointless waste of human life, would believe in objective morality, and George R.R. Martin, who had a working-class but fanciful childhood in suburban New Jersey would view morality as so ambiguous. Perhaps the answer to this mystery of human nature is that objective morality is a survival technique for those who face truly horrific conflicts, but likely it is more complex.