I used to do between 30 and 50 weddings a year, and you’ll encounter a whole spectrum of things.
Speaking now of Catholic churches specifically, I consistently find that the Wedding Coordinators are far more strict/intolerant/close-minded that the Priests themselves. The Wedding Coordinators are fond of saying “Father won’t allow so-and-so.” However when I go over their head and talk to Father himself, usually it’s fine.
This is particularly true when it comes to the uilleann pipes, which the Irish Priests know all about and often are very fond of, and the American Wedding Coordinators are ignorant (they think you’re talking about the Scottish pipes, always). Many dozens of times the Wedding Coordinator has told me that “Father doesn’t allow bagpipes” and Father, in fact, was delighted to have them.
About tunes, the Wedding Coordinators will usually tell you that only Sacred music is allowed during Mass. So you end up playing Pre-service and/or Post-service music. Many’s the time I’ve had to assure the Wedding Coordinator that I have a sufficient repertoire of Sacred music (including many of the currently popular Catholic Hymns). Father himself is usually more open-minded, for example one couple wanted Fields of Athenry and the Wedding Coordinator said absolutely not and Father said he would be delighted if I played it, it was his favourite song.
I can get trickier outwith the Catholic Church for this reason: many Denominations have a one-and-only official Hymnal, and some Churches require that ALL music played within the Church be from that Hymnal. This is no problem, I assure them, because I have a large collection of such Hymnals and I’m careful to play only things contained therein, when playing at a Church like that. (The LDS is one.)
It may surprise some that the Catholic Church has no such thing. Anyone can print a “Catholic Hymnal”, there are dozens of different ones from various publishers, so the concept of what constitutes “Sacred music” in a Catholic Church is fairly elastic, especially since Hymn-writers often use secular melodies for their songs.
Jewish services can be tricky too, and I always discuss my music beforehand with the Rabbi. Luckily I play a number of Jewish folk-songs.
Bottom line, a good talk with the Minister/Pastor/Priest/Rabbi beforehand is always a good thing.