Sibelius (including the violin concerto) and some fine symphonies), Gershwin, Copland, Elgar and Bernard Herrman are examples of good 20th century “classical” music.
Things do tend to get sparse after 1950 unless you have a high boredom threshold.
I’m willing to admit I could be wrong on how established postwar music is in the repertory. I went and had a look at some of the recent programs from the Boston Symphony (an orchestra hardly known for its avant garde tendencies), and there was a surprising amount of newish stuff. How established this stuff is can be hard to say, but at least it’s out there.
For the post-1950 stuff (or even post-1940), they may get programmed at concerts, but do the get in the regular rotation, i.e. played more than once or twice?
There are pieces like Bernstein’s Candide overture (a fine piece - I hope I never hear it again :)) but those are few and far between.
I know our local Symphony trots out the obligatory new work by a Canadian composer usually for the first piece of the concert and everybody suffers through it knowing that they’ll never be subjected to it again.