Many Jewish New Yorkers observe Christmas Day with a Chinese dinner. This year, the New York Festival of Song is offering what may soon become another Jewish Christmas tradition.

"A Goyishe Christmas to You!," which takes to the stage at the Kaufman Center's Merkin Hall on Tuesday and Thursday, features a roster of singers—including mezzo soprano Stephanie Blythe and Broadway star Judy Kaye—performing Christmas tunes written by Jewish composers. Among them are familiar classics,...