Would it be bad to make up a mythology for a fantasy story? I have thought hard about it, and realize that I could try and make the story cleaner (no pre-marital sex, no details of sex, no extreme violence, no profanity), but because it is a different universe, it will have a set of gods and goddesses similar to that of Greek mythology. I have been outlining this story for several years, but have not written it yet. Should I write it or just dump the ideas?
The problem with Greek mythology is that it saw gods as nothing more than superhumans. They had all the flaws of humans and their sins, but it was justified because they were supposedly deity. "For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse, because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened. Professing to be wise, they became fools, and changed the glory of the incorruptible God into an image made like corruptible man -- and birds and four-footed animals and creeping things" (Romans 1:20-23). Ultimately Greek mythology promoted and glorified immorality and, worse, attributed such to the divine.
I don't know how key these characters are to your story but have you considered the writings of C. S. Lews, J. R. Tolkein, or Stephan Lawhead? Each created fantasy worlds without stooping to a concept of gods who weren't divine in the true sense of the word. More, they managed to create worlds in which Christian principles and ideas, even those about God, were promoted.
The question to ask yourself is whether someone reading your story would be inspired to seek out righteousness or understand Christianity better, or would it give doubts that perhaps the idolatry of old was actually right.