Eid al-Adha is a sacred Muslim holiday celebrating the readiness of the Prophet Ibrahim to obey Allah.
To have “free from cruelty” Eid al-Adha means to make sacrifices without cruelty or slaughtering animals. Muslim vegetarians and vegans already practice ruthless sacrifice, using their free time to volunteer for charitable purposes, donating money or vegan food to those in need, or discarding their greed and selfishness.
The word “Islam” in Arabic comes from the infinitive sa-la’ma, the root of the word salam (peace), and salam is exactly what it means to celebrate the holiday without cruelty.