Speculative metaphysical theories are compatible with science because they are unprovable and, if true, "override" science as the true cause of the laws of nature and the world. However, this is trivial and uninteresting because we don't have good reasons to take any of these speculative theories seriously in the first place.
Insofar as supernatural/mystical beliefs correspond to testable claims about the world, these beliefs are clearly incompatible with science. First, they are not backed by evidence. Second, the combined efforts of anthropology, history, and neuroscience have built a compelling model of how people come to believe such things.