Traditionally speaking, priests do. Catholics understand that verb applies to the priest in the sense of my Webster’s: “to perform (a ritual) publicly and formally.” In this, a priest actually conducts the significant acts of worship at Mass. So in the sense of baptizing, anointing, preaching, confecting the Eucharist, the priest is the celebrant, and the GIRM acknowledges this, referring to the role as the “priest-celebrant.”
But in the sense of Webster’s third definition, “to honor or praise publicly,” people also celebrate Mass. Sacrosanctum Concilium backs up this interpretation:
“Mother Church earnestly desires that all the faithful should be led to that fully conscious, and active participation in liturgical celebrations which is demanded by the very nature of the liturgy.”
… for how else does one participate in a celebration? By celebrating it, of course.
As long as we recognize some basic ground rules, acknowledging people as “celebrants” seems appropriate.
1. Many, if not most words about celebrants, are more political terms than expressions making use of the English language to describe a liturgical reality. In certain settings, proceed with caution, knowing that politics has coopted the language.
2. The goal is a laity fully conscious and active. Whatever gets them there the fastest, even if one must occasionally use terms one detests, is good. Offer it up, as they say.
3. For priests, the goal is leadership, teaching, and being respectful of the role to which God has called them. Be a presiding celebrant. Being a priest means praying on behalf of the people and praying for them. If I were a priest, I’d think about those people unable or unwilling to celebrate.
The ultimate goal, after all, is not using words to get the upper hand in an argument, but to effect the worship of God and the sanctification of God’s people.
Whatever gets us there, it seems to me.