As a moderator on Mythology Stack Exchange, I’d just like to clarify what we mean by “mythology”. I would define a mythology as a set of stories, generally created by one group of people, that explain a version of the history of a world — usually our world.
If I were to use the term in a religious context, then I could talk about a specific story from a religion being part of that religion’s “mythology”, or I could talk about how a story of the start of the world is a “creation myth”. The thing is, the term isn’t supposed to be pejorative — when using it, I assume nothing about whether or not the story happened or not. Things that have indisputably happened can influence mythology — for example, the mythological version of King Arthur was loosely based on a real person — but they are still mythology.
“Myth” did become pejorative, but I would assume that that’s because nobody believes that all the stories in all the mythologies in the world are true. Some believe that a small subset of them are true; others believe that none are true. But for most people, the majority of mythologies are just stories, nothing more. So “myth” became derogatory.
Hopefully, a follower of a religion should be able to describe their own religious stories as constituting a mythology, without being offended. I apologize for the misunderstanding.