The story you are about to read is true. Only the names and location has been obscured to protect the semi-innocent.
So I was a young seminarian attending a Mass at which a prominent person from another religion was in attendance. The presider, wanting to show how open, welcoming, and progressive we are decided to change one of the readings at the Mass to a reading from this very non-Christian tradition (along with some interesting rite and prayer from the honored guest after Communion.)
Now, I know there will be people who say, "Great! It is about time that Catholics stop naval gazing and open wide the doors to everybody. We are not so fragile that letting someone in to do something like this will make us fall apart. Get over it and broaden your horizons."
I am not one of them.
Now, don't get me wrong. I am not opposed to experiencing someone else's "scripture" or even witnessing their rites (within reason - well, my reason.) Just not at the Mass.
The Mass is the very epicenter of our covenant. The very epicenter of the marriage covenant is the "marital act." You don't (or should't) just let anybody into the bed with you in order to broaden your horizons and show how open you are. It is the same with Mass. The Bridegroom is giving Himself in the most intimate way to His Bride. That is why we don't have what was once called, "Eucharistic hospitality." You either are in this marriage or you are not. If you are, welcome. But there are no strange bedfellows here. (Did I just take the analogy too far?)
"In the readings," paragraph 57 of the GIRM states, "the table of God's Word is spread before the faithful, and the treasures of the Bible are opened . . ." These contain the words of love and longing of our Father for His children and of the Bridegroom longing for His Bride (aka salvation history.) They are the prelude to this most intimate moment between our God and us. Therefore, not only may we not substitute another faith's reading, we may not even substitute another Christian reading as has been done, for example, by music groups substituting a song for the psalms or having a reading of Dr. Martin Luther King replace the first reading on Martin Luther King Day.
Even where the readings are read during the Mass is not something with which to trifle. These readings belong to the Church and we have a right (and a duty) to them. Therefore, in Masses with the people, says paragraph 58, "the readings are always read from the ambo." (Funny, my computer kept changing ambo to Rambo.)