First, there is not scientific research that concludes that the usage of incense is carcinogenic. Second, most churches are large and airy, and the fragrant smoke dissipates as quickly as it is used.
Incense has a long tradition in the area of worship. Not only did pagans use this, but Jews in the Temple service employed incense at the sacrifice of the animals.
Psalm 141 makes an analogy of incense and prayer when it says, “like burning incense let my prayer rise to you O Lord.” Moses commanded that in addition to sacrifices of animals, incense should burn before the Ark of the Covenant, which contained the Ten Commandments. The sweetness of incense reminds the worshipper of the sweet mercy of God.
In the Middle Ages, incense had a more practical use. Churches, cathedrals, and monastery chapels were often used as hospitals, and poor hygiene resulted in smells which were less than heavenly. Incense was employed as an ancient form of potpourri. In the Shrine of Saint James of Compostelo in Spain, one of the oldest and most traveled to pilgrimage sites, a huge thurible (incensor, a metal container on a chain that burns hot charcoals onto which incense is placed and burned) that swings from the rafters of the church is in constant use.
The Church has always used incense in the Liturgy during the Holy Sacrifice of the Mass, the benediction of the Most Blessed Sacrament, and the solemn celebration of Vespers. Biblically, it was one of the three gifts given to the Christ child by the Magi. It symbolized the royal priesthood of Jesus.
At Mass, incense is burned at the four presences of Christ—the proclamation of the Gospel, the gifts that become the Body and Blood of Christ, the priest, and the faithful. At funerals the body is incensed, because it was the Temple of the Holy Trinity through baptism when the person was alive.