According to the minhag I follow, one who is not a talmid chacham should not study Jewish mysticism (maase merkavah, heichalot, kabbalah, et c.). Following this, would one be able to read non-Jewish mystical texts (for non-religious purposes, of course), or would the same restrictions apply?
Non-Jewish mysticism is a very broad subject indeed. Almost every religion has something to teach on this subject, and a big part of this study has been influenced by the eastern religions, so you have to be careful with what you read.
Mysticism within the Abrahamic faiths should be fine as they do not constitute sifrei minus since they all believe in a personal god. However, Mysticism as has been taught by the eastern religions may constitute minus since its conception of god is wholly different than ours and, at least traditionally speaking, their ideas would be considered heretical according to Jewish law. (we can still make a case to allow it, since they do not promote a certain ideology, they merely discuss their mystical experiences and how to attain them, but that would be controversial indeed).
As for the waste of time aspect (which @ezra pointed out) it is not an issue at all, since it is a study of a particular wisdom of the gentiles and is part of the sifrei chachma (ספרי חכמה) which are permitted באקראי just like the study of philosophy and science.