moose, priest's horsehair flapper, elk
麈 centers on a large deer-like animal: a moose or elk. The meaning extends to a priest's horsehair flapper, likely because such flappers were made from the animal's tail hair.
麈 combines 鹿 (deer) with 主, which likely provides the sound. The character originally referred to a type of deer, specifically the moose or elk, and later extended to a fly-whisk made from its tail.
A deer 鹿 with a master 主 inside: picture the master of the deer family, a large moose or elk, standing proudly. Its tail hair is used to make a priest's flapper.
For シュ, imagine a shoe made from moose leather: shoe -> シュ, and the moose provides the material.
priest's flapper made from the tail of a large deer; long stick with the tail of a large deer attached