The religious rites involved in the festival are entirely Taoist
The supreme god worshipped in the shrines of Phuket is the Jade Emperor, or Yok-Ong Songte as the local people call him. He is the supreme god of Taoism.
The gods invoked to preside over the festival are called "Kiu Ong", which means "Nine Heavenly Kings". Originally, the nine kings meant the gods of the sun, the moon and seven other heavenly bodies. They should still be so. But they are now interpreted also to mean seven Buddhas and two Bodhisattvas. This is an obvious attempt to give the festival a Buddhist colour to broaden its appeal.
In short, the Vegetarian Festival is a festival to clean the body and mind. And it is a bonus to visit Phuket or other participating provinces during the festival period. Even if you do not like noise and crowd, you can have a glimpse of this event and then continue to enjoy your holiday in the usual way. The beautiful nature is not disturbed and is always ready to welcome you.