So while it is true saying: Character xyz IS chaotic neutral, its up to the player to interpret what this means.
D&D games almost always ignore the Law and Chaos axis as well. They only focus on Good vs Evil.
I will give credit to Pathfinder: Kingmaker for that, however they didn't split them, so you were forced to choose opposing options. I'm glad to see that will be changed with Wrath of the Righteous.