I think one of the problems with using secular music, especially classical, is that many of us associate certain pieces with secular activities, ad campaigns, etc.
An example is Copland’s “Hoedown” --it’s also the “Beef Music”! I think a lot of people older than 40 think of beef whenever they hear that music. (Also, I can’t imagine why Copland’s “Hoedown” would ever be used in the Mass!)
Much of Mozart’s music has been used in movies. Actually, a lot of classical music has been used in movies. I believe many of the Beethoven pieces were used in Clockwork Orange, a very disturbing movie done that I saw when I was in college–and it still bothers me.
My husband finds any Baroque music “frantic” and “nervous.” He hates it when I practice Bach or play it at church (organ). Just goes to show that even though many people consider Bach the epitome of sacred music, there are those people who can’t handle it in sacred settings.
I’m not really sure if this is what the OP means by “local classical” music. My first thought was “O God Beyond all Praising,” set to that gorgeous Holst music–I LOVE IT! But I have talked to others who don’t like it at all, and find it just as uncomfortable as hearing the Beatles’ "Let It Be’ sung in church.
I have come to the conclusion that there is no music that is the Definitive Music for Mass, and that we need to keep an open mind and be tolerant of the tastes of the local parishes around the world. Hopefully their bishops are approving whatever is played.