"T'row da bum out!!" The Music at a funeral, Rosary, or memorial service is for the family--not the accompanist. Because the same type of Music every Sunday is boring, a good church Musician is one who is capable of performing Music of most any style, just as a good Musician is one who can perform rock, classical, folk, Irish, Swedish, American traditional, Bebob, various gospel styles, etc., etc.
WYSIWYG may be right about the organist being too intimidated, otherwise the yahoo doesn't have ground on which to stand. They guy obviously is quite uneducated because one of the two most popular settings of "Ave Maria" uses the Bach Prelude # 1 in C major from the Well Tempered Clavier with an added melody.
   The minister or church board should not allow this type of censorship. I would have found another Musician!
   
    By the way, I am not nor was I raised Catholic, and am often called upon by many Catholic folks who presume that I am because I know all the usual "literature," sing very good Latin, and know lots of the old Irish songs from the Ould Sod through Tin Pan Alley & beyond. I'd rather sing in Latin that any other language--it makes one's voice sound the most beautiful.
Oh yeah, & I've done Music in regular services for Protestant (lotsa flavors!), Catholic, Jewish, Greek Orthadox, Buddhist, Native American, & was even hired a couple of times to play straightforward Bluegrass at a New Age church!