Believe it or not, but you can easily get a friction fit tight enough to hold a three-sided finished column against the wall which slides over wall-mounted vertical strapping. It's also easy to make with a jig to get a consistent, tight fit.
The other "attached but removable" alternative uses Velcro on the edge which will be hidden by acoustic panels and whatever else butts up against the sides of the column. Only four or five pieces on the wall-facing edge of each side has plenty of holding strength. If you need the cleanest look, the alternate Velcro mounting method is to attach a separate piece of strapping on the inside sides of the column that, when put against the wall-mounted strapping, gives you two flat surfaces that will hold the Velcro in opposition. I am taking this approach with my columns because I will be preserving access to the RGB LED lighting and the alabaster bits.
Most importantly, neither method will rattle.