That is why I used “modern”, what was avant garde in prior generations (Stockhausen, The second viennese school and 12 tone, minimalism) is now old hat while these days it is other things considered ‘avant garde’ shrug.Depends on what you mean by conservative,conservative these days could mean being locked into 12 tone music/serialism, minimalism and so forth, if you mean they push writing fugues and tonal music following neo classical or neo romantic forms,not so much. It happened that a lot of the young composers I heard at NYYS and with programs my son were in from programs like Juilliard and Yale SOM, and it was mostly either 12 tone and its variations or in the minimalist vein, I don’t think I heard one tonal piece in any idiom the more than a few years he did it. The OP said she was under the impression that the faculty at schools of composition were neo classical or soft core (I kind of laughed when she mentioned Korngold, there is an irony to that, it is only recently that his concert music, especially his violin concerto, is getting serious playing, because the schools of music decided his music was crap because he did movie music (his violin concerto is wonderful and technically challenging, and he based it on the scores he did for some of the pirate movies he did in Hollywood in the day.). Conservative these days means many things, I am sure a lot of young composers consider John Adams and Phillip Glass as old farts and 12 tone music as “finished”, much the same way that Boulez and Wourinam and Babbit decided anything before 12 tone was crap shrug.