Picasso's Guernica is my favourite example of art making a political statement. You'd probably have to know the background to it before understanding exactly what he was trying to say, otherwise it would likely be mistaken for just another abstract.
In 1937 the Nazis bombed a small Spanish village at the behest of Spain's fascist dictator, Francisco Franco - good friend of Hitler and, later, the United States. Guernica represents the fear, the chaos, and the senselessness of that bombing. Beyond that, the imagery in Guernica is so striking that I think it causes the medium (oil) to stay at the back of the viewer's mind or even go entirely unconsidered.
A more contemporary example might be Andres Serrano, dismissed by some critics as superficial (I can't wait until those critics hit the world with their masterpieces and show everyone how it's done) but which I find brilliant; not for their shock value (he has combined various bodily fluids with, among other things, religious iconography), but for the fact that the medium often isn't readily apparent in his work, only in the titles of his work. If his abstract pieces had been created through a more traditional medium, I think they'd be held up and appreciated at the mainstream level. I think Serrano uses a combination of artistic skill and business acumen (the recognition that controversy sells) to simultaneously remove the medium from the viewer's eye and yet still use it to promote his work.
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