At the end of his life, in the years he wrote War is a Racket, I’d describe him as an unaffiliated social democrat. He ran for Senate in 1932 as an “Independent” (that is to say non-machine) Republican on a platform that included support for major public spending, a federal jobs guarantee, strong support for labor unions and a federal old-age pension (as well as continuing Prohibition). He voted for FDR that fall. His last presidential vote, in 1936, was for the Socialist Party candidate, Norman Thomas. But he was never a member of any left party. CPUSA head Earl Browder shared your assessment that he “had no conception of politics” but was “just a soldier fighting for the soldiers.”

I detail all this with sources in my new book on Butler, Gangsters of Capitalism: https://us.macmillan.com/books/9781250135582/gangstersofcapitalism