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I think the main thing is that generic mindfulness exercises don't have a devotional aspect, i.e. no worship or veneration of deities, prophets, saints, spirits, or the like. A lot of people in cultures influenced by Abrahamic traditions don't think of something as "religion" unless it has devotional practice.

An important exception is that some Christian fundamentalists regard any form of magic or mysticism other than God's miracles as being inherently Satanic. This can even extend to fictional systems of magic (as in fantasy novels or RPGs), which may be regarded as an obfuscated form of the real thing.