He was born in Russia, fought in the Great War for the Imperial army, served in the anti-Bolshevik White army, and then fled the country for China. He eventually came to the USA, painted murals and canvas-based paintings, and taught art at Stanford University. As part of his mural painting, he worked with Diego Rivera which, perhaps along with other factors, led him to left-wing politics. Following the death of his wife and retirement from Stanford, Arnautoff moved to the Soviet Union, dying in Leningrad.
So he "progressed" from anti-Bolshevism to leftism, depicting proletarians while teaching at an elite university. I'd call it a nice trick, but aside from the anti-Bolshevik part, the rest isn't uncommon today.
As for his mural style, Arnautoff was mainstream in his Modernism-lite technique. His approach to subject matter was essentially representational, but tempered by modernist conventions so that picture-plane flatness, considerable simplification, and a little distortion of forms were included. The result has a cartoon-like character to my eyes. But that style was a 1930s artistic fashion.
His major work was a mural titled "City Life" that was part of the Coit Tower mural set (that was recently restored). It is featured in the images below that include a few other works intended to provide some sense of his artistic range. Click on images to enlarge.