In the United States, applause/clapping is the way to say a corporate “Thank you.”
In many situations, e.g., a crowded Mass filled with families, small children, and the elderly, it is impractical for all of these folks to make their way to the front and say “Thank you” to each and every member of the choir, the director, and the instrumentalists. Applause is an appropriate way for the congregation to express their thanks to those who have sacrificed their time and donated their talents to serve the Lord Jesus and His children.
Although the Sacrifice is sufficient and praise-worthy without music, music does help to make the experience of the Mass more real and vital and emotional for most people.
In the story of the ten lepers, only one leper returned to say “Thank you” to Jesus. Jesus did not condemn the leper, but rather, praised him. It is GOOD to encourage each other, to be courteous and charitable and kind to each other. I cannot understand how so many of you twist something good into something bad, and how you can ascribe evil to good. We used to have an expression in the Protestant church–“They see a demon behind every tree.”
In the U.S., where uncivility and rudeness is the rule rather than the exception, I think that ANY expression of the good old-fashioned phrase, “Thank you” is right and wholesome and charitable.
What better place to say “Thank you” than in a Holy Sacrifice of the Mass, where we come to give thanks to Jesus for His sacrifice and to receive Him in Holy Communion even though we deserve nothing but death?
Giving thanks to our brothers and sisters in Christ who we can see and hear helps us to learn to give thanks to the Lord God, Whom we do not see or hear.
Those of us who play and sing the music of the Mass do so ONLY because Jesus has given us the talent to do so. JESUS is singing and playing through us, using our voices, our hands, our feet, our minds–when you applaud us, you are really applauding HIM!
We could all use a lot more tangible expressions of love. The last few months have been pretty bad for me, between work and other involvements where love is hard to find and people are all too-ready to give me the finger instead of a round of applause. I have been depressed and discouraged all too often. It is a wonderful encouragement to me when someone thanks me for my music, either through their words or their applause. It means the same thing–“Thank you.” Good words, appropriate for Mass, because love is what the Mass is all about.
Jesus Christ has commanded us to LOVE ONE ANOTHER. To love each other, to say thank you to each other, does NOT take away any of the glory that belongs to the Lord, but rather, GIVES Him more glory. When Christians love each other, it demonstrates the POWER of the Sacrifice of Jesus on the cross.
Finally, if it doesn’t seem to bother the priest, why does it bother you? Isn’t HE the ordained authority in the local parish? Share your concerns with him. I’ll bet he’ll say something similiar to what I’ve said in the above paragraphs.
But, come to find out, it’s monsignor’s way or the highway. 
So, eventually, it came to make no difference to me. 
It’s not appalling to me that the people applaud after Mass. The choir is a ministry, true. However, it’s also music practice and, yes a bit of performing as well as trying to give true feeling and deliver the meaning of what we are singing. Sometimes it’s inspired, sometimes it’s more of an effort to do some of the music. Our choir director is an inspired professional musician of a high caliber. There are two semi-professional singers among us who give strong support to all of us. Personally, I try to be inspired, sing to the Lord and project that inspiration. I am not always successful in doing so.