This line of thought has its origins in Artforum, where, under the editorship of John Coplans, the magazine swung heavily towards identity politics, and Abstract Expressionism was out of favor. Pollock was not singled out, though; all of Abstract Expressionism was accused of being an ideological weapon in the cold war. See Max Kozloff, "American Painting During the Cold War," and Eva Cockcroft, "Abstract Expressionism, Weapon of the Cold War," both published in Artforum in the early 1970s and reprinted in Francis Frascina, ed., Pollock and After, The Critical Debate (1985).
Whatever you want to say about Pollock and Greenberg (and Newman, etc.) they were hardly apolitical--or inoffensive. Greenberg was a socialist Jew who at one point edited Partisan Review; Newman was an established anarchist and wrote prolifically about it; Pollock began painting as a social realist and admired Rivera. Their work was reviled and misunderstood by many in its moment. How, or whether, the paintings were subsequently appropriated by American power afterward is debatable (the Frascina book is the best resource for this), but the conspiracy theory angle--Pollock as a covert operative--is unlikely.
For a substantive, historical account of how Abstract Expressionism was used ideologically in a world context, the best thing I've read is on Barnett Newman and the 1967 World Fair in Bruce Barber, ed., Voices of Fire: Art, Rage, Power, and the State (1997), especially the essays by John O'Brian and Serge Guilbaut. The best account I've read of the particular style of politics at play in AbEx painting is the one offered by TJ Clark in the last chapters of Farewell To An Idea. There's a great argument on Pissarro's anarchism as well.
Sorry for throwing a bibliography at you! Those are the places you'd want to go if you wanted to put it together for yourself.