I see what you mean, though I still prefer Mozart... When did the shift occur, because surely at the time of its composition, Mozart's Requiem was licit?
My impression was that culturally the shift happened in the 12th and 13th centuries with the beginnings of polyphony. Music was never highly regulated, and most of the music used at Mass was a matter of local custom.This can be shown by the wide variation of certain well known chants. Thus when extra voices were added, this also was a matter of local custom, some did this, some did not, and those who did had various ways of singing.
There were undoubtedly some objections that the new forms with extra voices were not proper, but music was generally a laissez-faire commodity for a long while.
At the Council of Trent there were some loud objections from those who wanted to forbid any polyphony and allow only Gregorian Chant. These purists probably had a very good intention in trying to reign in some abuses in the musical realm, but when it was decided to allow polyphony without detailing some restrictions, this was an invitation for composers to write whatever they desired (so long as it pleased their patrons).
Thus it wasn't really a matter of Mozart's Requiem being "licit" as much as until the 19th century, no one loudly objected.
And St. Pius X wasn't the first to try to regulate sacred music and art, but he was had the most lasting effect and was the most direct. By the early 20th century it was clear that most "Sacred Music" was just secular music with religious words and Gregorian Chant, the only music that the Church herself calls her own was rarely, if ever sung outside a monastery.
The standard that St. Pius X was trying to set is that Sacred Music should be different and set apart from secular music. Don't get me wrong, I quite fancy the Mozart Requiem, but at the same point in time, there is very little stylistic difference between the Requiem and Magic Flute, save for some thematic elements. The Requiem (as a Mass) is perhaps the most liturgically appropriate of all of Mozart's Masses as well. An orchestral Mass is perfectly permissible for a feast, but most of Mozart's festal Masses are so long, the words repeated and twisted in so many ways and the movements proliferating in such a manner that they turn the Mass into a concert at which some liturgical ceremony is happening in another part of the building.
Of course the Archbishop of Salzburg did use many of these Masses, but I am certain they made for Masses where the Mass itself became secondary to the music.