Police concluded there was "insufficient evidence to provide a realistic prospect of conviction for any offence" after reviewing video and audio recordings.
The investigation was launched in June after officers examined footage from both Kneecap's and punk duo Bob Vylan's sets at the festival.
Avon and Somerset Police confirmed they are still investigating comments made by rapper Bobby Vylan, who led chants of, "Death, death to the IDF".
A Kneecap member had joked about fans starting a riot at a bandmate's upcoming court appearance related to a terrorism charge, later clarifying it was for "love and support, and support for Palestine".