balei chayim are muktza. If the animal is a pet for a child like a toy a parrot etc & its daily practice is to be on the bal habayis' shoulder, is it still muktzeh?
Answer:
All animals (including pets) are muktzeh on Shabbos (Shulchan Aruch 308:39).
Although the Mishnah Berurah permits moving a muktzeh item with one's body, in this case carrying the parrot on one's shoulder is the "normal way" of holding him, and this should therefore be avoided on Shabbos.