Your comment reminds me of my frummishe Yid choral director from my college days. I was startled when he told us the repertoire for the year - two performances each of Handel's Messiah, a Vivaldi Gloria, Faure's Requiem, Berlioz' Requiem, and as a vocal exercise, Brahms' Deutsche Requiem.

But he had no qualms about taking the podium in the Albany Cathedral wearing a yarmulke.

And when we performed Bernstein's Chichester Psalms, in Hebrew...it was also in a local cathedral.

None of the temples had pipe organs.