Councillor Elizabeth Threlfall said the inclusion of Bob Vylan on the “bill is a mistake”.
She said Wiltshire Council, as the licensing authority, had a duty to protect children.
“Bob Vylan are an offensive act,” she told the hearing.
“Violent views are part of their unique selling point.”
Following their Glastonbury appearance, the band was dropped from a number of festivals and performances including Radar Festival, Kave Fest, and a US tour after their visas were revoked.
Avon and Somerset Police also launched an investigation, but ruled no further action would be taken as it did “not meet the criminal threshold” for prosecution.