I don’t know the official answer to the OP’s question, whether a cantor must be Catholic. In my opinion, for an occasional event (wedding, funeral), a trained and properly disposed non-Catholic is acceptable, but I think that all persons who regularly serve in a ministry at Mass (EMHC, lector, music director, cantor, etc.) should be Catholic.
Having a non-Catholic in such a position is potentially problematic, because people in these ministerial positions are representatives of the Catholic Church.
Case in point: The music director at my parish is Lutheran, and she has many times made comments to choir members that she doesn’t agree with this or that Church teaching. The latest was at a choir rehearsal before Christmas where she vehemently said, “I don’t believe all that Mary stuff. I know that Mary and Joseph had sex, AND that they had other children.”
Several choir members nodded their heads in agreement, for after all, she is a “person in authority.”
As I said, I don’t know the Church’s official stance on this issue, but having a non-Catholic cantor has the *potential *to cause scandal.
'thann