What religion is Guanyin?

Both Taoism and Buddhism.

1. In Taoism, Guanyin Bodhisattva is a poet and one of Twelve Jinxian's disciples under the Buddha's seat in the early Yuan Dynasty. She is also known as Cihang Fairy Valley, Cihang Purdue Buddha and Cihang Purdue Tong Yuan Freedom Buddha. It first appeared in the book Zi Zhi Tong Jian in Qing Dynasty.

2. Avalokitesvara, one of the three great Buddhists, is called "Avalokitesvara".