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And while we’re at it,
Obviously saining is the only one of these I have actual experience with, so feel free to add expanded resources for the other two or for something else entirely!
So the cleansing of a space with smoke is called smoke cleansing. It is done in many cultures and religions and is not a bad thing. The appropriation comes when you call it smudging. Smudging is a large ceremony withing a tribe that is more than just burning herbs.
Smoke cleansing is fine.
Calling it smudging is not.
The act of cleansing with smoke is not appropriation.
Calling it smudging is appropriation.
Though I would like to add that white sage (what those store bought sticks are usually made of) is WAY over harvested, which is bad for those Native American tribes that NEED it for their sacred rituals. So if you must use sage, look into using a different kind, or even grow and dry your own to make your own bundles.