Any composers of classical music who wrote in the 20th century?

It was a big period for Russian composers, who all had to cope in one way or another with the Communist Party after the Russian Revolution. Someone else mentioned Shostakovich. Also check out Rachmaninoff, Khachaturian, Stravinsky. Prokofieff.

Two prolific English composers who come to mind: Vaughan-Williams and Rutter. Among their many works you may easily find some which were commissioned for political purposes. Rutter is still active.

Just thought of Benjamin Britten, another English guy. You might find his "War Requiem" fits your description, as he was a pacifist.

If you want something slightly off the beaten path, you could try someone like George Butterworth, who set a number of texts of A.E. Houseman's "A Shropshire Lad." Depending on how creatively you want to interpret "political message," you could focus on composers like Rubbra or Messiaen, whose work is permeated throughout by deeply held religious and philosophical beliefs.

Aaron Copland...I don't know of anything political he wrote, except for that piece about Abe Lincoln. He also wrote a piece about Billy the Kid, which has to do with American History.

TECHNICALLY the classical period was over 200 years ago anything written in the 20th century is contemporary

but Shostakovich wrote his symphonies (like the 5th especially) under speculation of the USSR. In his 5th symphony he mocks them and he was definitely under fire. you should check more about him out