If there is one thing that the Aeternalae DON'T believe, it is in the instrument of destiny. Indeed, destiny and karma (the latter at the least in a long-term sense) are generally conceived to be ningen interpreations of the mechanations of the Second Realm.
As Aeternalae regularly flaunt the rules of the Second Realm, it is understandable that destiny is regularly altered by them. In fact, the influence created after the creation of several new etones completely rewrites "destiny" as might be conceived in ningen thought. So while destiny exists, it is not as set in stone as ningen are regularly led to believe. Free will, though illusory on a certain level (after all, one is conditioned to react to certain things in certain ways) does exist on the larger scale.
As for karma however, the significance of such is diminished, due to the assumption of the universe that people are inherently good (rather than inherently evil or a blank slate, "tabula rasa") but rather easily hurt and confused. As a result, people who are "evil" are not punished by some overriding cosmic force. Instead, they are to be healed, which is one thing that the Aeternalae strive to do, even if it is by their own methods.
Short-term karma, in particular, karma in this life, is not to be completely ruled out however. After all, it is a known fact that people are normally influenced by your own actions, and as such, the Golden Rule very much applies. so while good things often happen to good people, and bad things happen to bad people, it's not necessarily due to predestination of their actions.