Jimmy Cagney, despite his role as "Yankee Doodle Dandy," was known as a pinko in Hollywood in the 30s, and as I understand it took the role in Yankee Doodle Dandy in part to overcome that reputation as best he could. He may have moderated his politics in old age but I don't believe he could ever have been described as conservative.
Peter Ford may know something I don't know, but that's what I recall reading about Cagney, anyway.
No less a source than Gordon Liddy describes him as a conservative. As a child Cagney had to constantly scam his way into getting a meal. Liddy quotes him as saying "When government gives you money with one hand, the other one is taking away your dreams"