My sister and brother-in-law sing with the St. Ann Chapel Choir. The choir specializes in Gregorian Chant and Renaissance Polyphony (John and I were privileged to have them sing for our wedding and I sang with them in the summertime during my college years).
I've always found it interesting that a number of non-Catholics sing in the choir and attend the Masses the choir sings at because they love the music so much - the same music that was promulgated as the norm by Vatican II but is rejected by vast quantities of Catholic Church music directors in our day and age. I just can't imagine non Catholics joining Catholic choirs to sing Haugen and Haas. Can you?