The title and the plot is a spoof of the hillbilly feud between the Hatfields and the McCoys in West Virgina in the late 19th century.
The Bugs was a parody of The Beatles and their music.
When the Hatrocks leave the Flintstone residence for the Worlds Fair, they encounter a billboard advertisement for Bug music with the 4 Insects playing at The Worlds Fair. In reality in 1965 when this episode aired, The New York's Worlds Fair was about to begin its second season in Flushing Queens New York and The Beatles would play in concert at Shea Stadium, across the street from the NY World's Fair. The 4 Insects were a clear parody of The Beatles with their "yeah, yeah, yeah's" and mop top wigs.