Oh, come on, this whole thing is silly. I've never heard of any rule that music in a ceremony can only be used if it was written by a Catholic. Every trad church in existence probably sings "Joy to the World" at midnight Mass, which was written by protestants, both in the words and in the melody. Probably music by Bach or Handel have been used in Mass.
Where did I say there was a "rule"? I just it's inappropriate and unbecoming to use the works of non-Catholics during Catholic Liturgy.
Again, some of you guys think that just because something was done pre-V2 or by "Trads" ... singing "Joy to the World" ... that it's appropriate. Not that I myself ever heard "Joy to the World" actually DURING the Catholic Mass. I've heard it only before Mass when various Christmas songs were sung but never during a Mass / Liturgy.
One of the FIRST things St. Pius X did after becoming Pope was to ban a lot of aberrations that were already starting to creep in. This has been done repeatedly at different times in Church history ... and will likely have to be done again.
So, for instance, it's quite clear that women should not be engaged in Liturgical singing ... clearly taught by St. Pius X. One could argue, as I do, that Missa Cantata is just a Low Mass that's decorated with some quasi- or extra- Liturgical singing. One clue is that the Altar Servers actually say the responses that are sung by the choir. But with a true Liturgical choir, they do not, as they actually take on the role of the Altar Servers. But I've seen quite a few actual High Masses (with priest, deacon, subdeacon) with women singing in the choir ... banned by St. Pius X, but ignored by Trads.
So the next Pope will also have to re-instate a lot of the measures that were instituted by St. Pius X but universally ignored.