I think calling it smudging is closed. Burning the sage or palo santo for cleansing is not a closed practice. It’s my understanding that “smudging” is a Native American ritual for some tribes & it’s not always Sage that is used.
I will say that I usually don’t call it smudging, I call it cleansing my space.
@Francisco or another mod may have more guidance for this one. I may be confusing 2 practices.