GREENWICH, Conn.—Synagogues have long been a part of this wealthy suburban town, but as recently as the 1950s it wasn't uncommon to find restrictions barring Jews from certain neighborhoods and country clubs.

Now Greenwich—still known for its blue-blooded families and sprawling mansions—has at least four formal Jewish congregations serving this town of 61,000 residents. Jews make up about 11% of its residents.

And...