There were so many with that theme in the Seventies!
One that comes to mind is "The Lolly-Madonna War" aka "Lolly-Madonna XXX" (1973), starring Robert Ryan, Rod Steiger and Jeff Bridges.
"Moonrunners" (1975) is a contemporary setting as far as I know. It's the inspiration/forerunner of "The Dukes of Hazzard" TV series. So, I'm not sure this is at all right. I'm thinking particularly of one though I'm not sure that will be right either.
"Moonshine County Express" (1977) stars Claudia Jennings, but I think it might be contemporary, too. She also starred in "'Gator Bait", but I don't think that was a moonshine movie.
"White Lightning" (1973) with Burt Reynolds deals with moonshiners but also is a contemporary setting, not the Thirties.
I'm still coming up empty as far as I can tell.
NOTE: "The Molly Maguires" is about the Irish-Americans' battle with coalmining companies and takes place in the late 19th century (1876, to be specific), so it wouldn't qualify. Moonshine isn't an element in that film though the fighting certainly is.