For 2,000 years, Jews have spent Yom Kippur, the Day of Atonement, in a synagogue abstaining from food and drink, fervently praying and beseeching God to forgive their sins.

This year, some rabbis, eager to woo younger people to High Holiday services, are holding programs in a beer garden, replacing deep reverential bows with goat yoga and celebrating the end of the season with glow sticks in a mosh pit.

“For...