A recurring theme in the Trilogy is that violence occurs during religious ceremonies or church-related events. I guess it's FFC's way of reminding us that religion and violence mix. For that matter, the opera he chose as a main thematic element in III is "Cavalleria Rusticana," which takes place on Easter Sunday and ends in a killing for "honor."
Martin Scorsese has a parallel shtick: In "Mean Streets" and "Goodfellas," violence often occurs when Italian music is playing on jukeboxes, radios, etc.

Yes, I thin that the Church was overused in GFIII, but I also think that having half the film take place in Sicily was overuse.

Having too much time in the party at the beginning in Part III was also overuse.