One of the approaches to Schnittke is to regard him in the same way as many do Shostakovich, i.e. in relation to the Soviet regime.
The difference is whereas Shostakovich had to respond to an ideology which was still vital, Schnittke’s music is more of a “hangover”, when the USSR had all but run out of steam. He is the “anti-Shostakovich” if you like (although his music clearly shares many similarities and Schnittke was hugely influenced by Shostakovich).
His early work is confusing, confused and aggressive; his later work is bitter, like Shostakovich’s, but tinged with a true gift for humour. It can often turn very quickly (not unlike that of Malcolm Arnold) which is either disconcerting or unsatisfying, depending on your point of view. However, unlike Arnold, Schnittke abandons tonality very readily, and is a tougher listen in many ways.
A couple of recommendations: his first Cello Concerto is an utterly typical work, abrasive, challenging and at times moving, and it is given a magnificent performance by Natalie Gutman on Regis. His first Concerto Grosso (he was the twentieth century’s most prolific composer of concerti grossi, by then a largely defunct form) is a magnificently witty piece, not to be missed.
It’s true that he was not Shostakovich, but only Shostakovich managed to be Shostakovich. However, Schnittke was, like Shostakovich, trying to find a way to write “his own music” at a time when the regime in charge of the country wanted dismal saccharine pap like Dunaevsky. Schnittke succeed in avoiding that kind of dross, and remained firmly his own man in spite of pressure to write dumbed-down drivel.
Many composers of his generation felt that the expressive vocabulary of previous generations could no longer be taken at face value. Some responded by starting again from scratch, some by treating this vocabulary in a distanced, ironic or playful kind of way, while Schnittke responded (as I hear his music anyway) by amplifying and worrying obsessively at those expressive gestures until they began to take on some meaning again, albeit often a bitter and even hopeless one.