Of all the mislabeling of entertainment that goes on, none sets me on edge quite like "sci-fi" referring to stories that contain the supernatural. I appreciate that authors don't feel obligated to confine their ideas into neat little categories (nor should they!) and that consequently none is adequate. I recognize that almost from the very start sci-fi, science fiction, bifurcated into stories based on the one hand on the "hard" science of experimentally-verified theories, and on the other hand on "soft" scientific or technological speculation. Moreover, a work's scientific "hardness" lies on a fuzzy spectrum because some of its ideas could be hard and others soft. If the work is episodic, then each episode could be different on the scale. I enjoy both hard and soft sci-fi, although I prefer that a story strives to stick to its chosen hardness rather than leaping sloppingly over the line and back.
My limit is really pretty simple: once a story is so soft on science that it includes the supernatural, its sci-fi credentials should be revoked at least temporarily. I'm okay with exposition like "the 'telepathic' race communicates with one another through radio waves". I'm not at all okay with "the being made of energy can create and transform matter at will". Or rather, I'm not okay with that character's story to be known as "sci-fi". Science's relevance to that story is slim.
The dividing line shouldn't be that hard to distinguish. If a story entails a concept that science contradicts, casts doubt upon, or dismisses from consideration, then the story shall not be deemed science fiction. If a story's suspension of disbelief involves jettisoning the conventional scientific perspective, then the story is outside science--beyond it, if you prefer. It's a supernatural story. Such stories might have value for any number of reasons, but worthiness of the "sci-fi" description isn't one.