In fact, I would go so far as to say that some people may use “faithful” on occasion to refer to religiously momentous events, but that they are intentionally spinning the original phrase that uses “fateful” for effect.
It’s a fateful day because it refers to a day when something occurs that changes the course of events or has tremendous consequences, as if it altered one’s fate. It would not make sense to speak of a day as something that possesses faith; none of these definitions applies to a day.