Catholics would not want to participate in smudging because it is shamanistic and therefore incompatible with Christianity.

Let me explain.

Although each tribe is unique in their spiritual beliefs and practices, generally speaking, smudging is a common Native American practice that is intended to spiritually cleanse a person, home, animal or object in order to bring them into harmony with the universe. This is based on the shamanistic belief that every object in creation, even those we consider to be inanimate, has a spirit.

Smudging is performed with smoke derived from the burning of herbs such as sage or lavendar, pine or cedar.  Practitioners believe the smoke attaches itself to "negative energy" and as the smoke clears, it takes the negative energy with it. Smudging is performed by waving or fanning the swirls of smoke around a person, object, or in a room that they want to cleanse.

Some practitioners also believe that the cleansing quality of smudging enables a person to communicate directly with the spirit world.

People are encouraged to "smudge" when their spirits are low, if they've been around someone who is sick or depressed, and during meditation and prayer.

But beware of another danger lurking in this practice! New Agers have thoroughly co-opted Native American spirituality, much to the chagrin of native tribes throughout the United States, so much so that the Lakota tribe actually declared war on them in the early 90's. For this reason, in addition to the shamanistic beliefs inherent in the practice of smudging, you will also encounter all kind so of New Age beliefs that may or not having anything to do with authentic Native American spirituality.

It's easy to spot the New Age in this quote from a Native American enthusiast: "The purifying smoke of sage, cedar or sweet grass is ceremonially fanned through the energy field to cleanse vibrations, attract positive energy, healing and protection."

Even though we respect the beliefs of Native Americans, Catholics have their own spiritual cleansing ritual par excellence in the Sacrament of Reconciliation. Through this sacrament we're cleansed of the sin that can cause a rupture in our communion with the living God. In addition, our communion with the Body of Christ is also restored. Regular confession of every day faults brings a wealth of other residual helps, such as enabling us to "form our conscience, fight against evil tendencies, let ourselves be healed by Christ and progress in the life of the Spirit." (Catechism No. 1458).

Who needs smoke when you can have all this?