I'm a bit older and grew up with Broadway and film soundtracks until I switched to rock (the Byrds' 5D was the first rock album I bought).

I had and enjoyed the Broadway original cast recording of The Sound of Music, with Mary Martin, Theodore Bikel, and Kurt Kaznar. I saw the movie in Cinerama with my family but never bought the film soundtrack, which is a bit sanitized (as is the script from what I can tell). The Broadway version has a song "No Way to Stop It" sung by two Nazis (including Baron von Trapp's fiancee), arguing that the Baron should accept the Anschluss of Austria by the Nazis as inevitable.

Authoritarianism vs. individuality / conformity vs. integrity is the major theme of the story. The convent represents a more benign form of authority, against which Maria is always (but not intentionally) struggling ("How Do You Solve a Problem Like Maria?"). The Nazis of course embody authoritarianism, and Baron von Trapp is somewhere in the middle until he falls in love with Maria and sees how she has won over his children. Art (music) is both metaphorically and literally an escape from tyranny / conformity.

A subtheme is experience vs. innocence--embodied in the Rolf-Liesl relationship ("16 Going on 17") , but since Rolf is a budding Nazi himself, it's clear that the story sides with the innocence of Maria over the jaded cynicism of the Nazis.

What's remarkable about the play is that it premiered at the end of our country's most conformist decade. Although McCarthyism was on the way out, there was (as your recent article on anti-Semitism in the old South points out) still a great deal of prejudice and authoritarianism, and The Sound of Music Broadway play shone a light on the perseverance of this spirit.

I would guess John Coltrane felt that the new directions he was exploring would provide a sort of escape from conformity and authority as well, and I wonder if he was inspired by the spirit of Lindsay and Crouse's storytelling as well as the music and lyrics of Rogers and Hammerstein.