Should seemingly arbitrary things like "play piano for Church" or "intramural badminton" go on M.S. or PhD applications in sciences/engineering?
No.

These things are by and large irrelevant. Everyone has hobbies, and many of these may be challenging, but the purpose of a graduate school application is to understand your background as a potential scientist.

At best, this will make someone go "Huh, neat, the oboe..."

At worse, it will make someone assume that you're either attempting to pad out a relative lack of accomplishments, or don't really know what you're doing.