Why does the Catholic Church require that only wheat bread may be used in hosts that are consecrated during Mass? Is it possible to use rice hosts or gluten free hosts? What about people with celiac disease?

The short answer is that the Church only uses wheat bread at Mass because Sacred Tradition tells us that Jesus used unleavened wheat bread at the Last Supper. The long answer to this question is found within our understanding of what makes any sacrament valid. A sacrament is an outward sign, instituted by Christ to bestow grace upon the recipient. All the sacraments have both material and formal components to them (oil and prayer in anointing, water and invocation of the Trinity at Baptism, bread and wine at Eucharist, etc…) The sacraments employ material things as channels of grace, actually bringing about the spiritual effects that they symbolize. Some materials are more conducive than others for serving a specific symbolic function. This fact does not render other materials inferior in intrinsic dignity--merely less fitting in their representative value for a given purpose. For example, when our Lord instituted Baptism, the sacrament of spiritual rebirth, he explicitly mandated water (see John 3:5). Indeed, only water is an appropriate physical substance for baptism, because more than any other liquid it is apt for signifying what it produces in the soul: cleansing from sin and regeneration into the new life of sanctifying grace. When it comes to the proper matter for bread, there are many references in Sacred Scripture to the use of wheat as being most suitable for the Blessed Sacrament. (See Matthew 26:26; Mark 14:22; Luke 22:19;1 Corinthians 11:23-24) Wheat is associated with being sown, fallen, crushed and buried, but then springing up for bread to feed multitudes. These are all symbols of Christ’s passion, death, resurrection and communion with his Church in the sacrifice of the Mass. We know that Jesus calls himself the “bread of life” (John 6:35, 48, 51). Furthermore, we recall that in John 12:24, during Passion week, he associates his own body to wheat, when he declares: “I solemnly assure you, unless the grain of wheat falls to the earth and dies, it remains just a grain of wheat. But if it dies, it produces much fruit.” Here we observe those symbols of sowing, falling, burying and rising applied by Christ to himself, who therefore becomes the “wheat bread of life” (see 1 Cor 15:20, 36-37, where Paul suggests something similar). Therefore, gluten free hosts or rice hosts are not permitted for Eucharistic consecration because they contain invalid matter. People suffering from a gluten intolerance or celiac disease may drink the precious blood at Mass or they may request to receive a low gluten host which contains just .01% of wheat.