Here are some early recordings with similar titles. I haven't heard all these, and I don't know if the songs are really related.

Riley Puckett, MAMA DON'T ALLOW NO LOW DOWN RIDERS HERE, Columbia 15261d, 4/11/28
Kentucky Ramblers, GOOD COCAINE (MAMA DON'T ALLOW IT), Broadway 8271, 9/30
Smiley Burnette, MAMA DON'T LIKE MUSIC, Perfect 13011, 5/28/34
Bill Boyd & Cowboy Ramblers, MAMA DON'T LIKE NO MUSIC PLAYIN' HERE, Bluebird 6235, 1/27/35
Ted Wallace & His Swing Music, MAMA DON'T ALLOW IT, Bluebird 6251, 1/17/36
Washboard Sam, MAMA DON'T 'LOW NO LOW DOWN HANGIN' ROUND, Bluebird 6355b, 4/3/36
Arthur "Big Boy" Crudup, MY MAMA DON'T ALLOW ME, Bluebird 34-0717a, 4/15/42?
Arthur Crudup, MY MAMA DON'T ALLOW ME, RCA 20-2509, 4/15/42
Jerry Irby, MAMA DON'T ALLOW IT, MGM 10580, 1949?