Chigurgh tells Carla Jean, "You didn't do anything. It was bad luck." He also offers her a coin toss. Are these gestures consistent with his worldview? If so, how? If not, how are these gestures inconsistent? Why then might he have made these gestures towards her? I believe him giving Carla Jean the coin is consistent with his view, but I need help with the how and why. I'm interested in the scenes with the gas station owner, Wells, the drug dealers, and finally Carla Jean.

Chigurh's behavior towards Carla Jean is certainly consistent with his worldview. Throughout the novel, Chigurh sees himself as a sort of messenger or personification of fate, and his offering each victim a coin toss before killing them further suggests this.
Back in the gas station passage, when Chigurh speaks to the attendant, he makes the connection between the coin tosses, himself, and his views on fate clear. "[The coin] has been traveling twenty-two years to get here and now it's here . . . you stand to win everything" (145). After the attendant calls it correctly, Chigurh spares his life and gives the attendant the coin, calling it his "lucky coin." 
Wells says of Chigurh in one passage, "These are not good odds. He’s a peculiar man. You could even say that he has principles. Principles that transcend money or drugs or anything like that." Wells believes that Chigurh operates solely on his principles and his belief that he is bringing fate to his victims.
Once again, when Chigurh speaks to Carla Jean, his idea that he himself is simply a messenger of fate becomes clear. He says, "When I came into your life your life was over. . . . You can say that things could have turned out differently. That there could have been some other way. . . . You're asking that I second say the world. Do you see?" (260). While many others (Wells, Moss, etc.) simply think Chigurh is insane, the novel never makes clear if he is delusional in his ideas.
Yet Chigurh is also a man who kills out of necessity to further his journey. When captured at the beginning of the novel, he murders a police officer to escape custody. He murders a passerby to steal his car. In the motel, he murders drug dealers who he believes has the money. Chigurh certainly is animalistic in a sense, killing to survive, and the police officer, the passerby, and the violent drug dealers are all threatening his survival.
Chigurh, then, operates as a messenger of fate, though he remains a character unafraid to kill for his own benefit.