The reason why there were Jewish country clubs was because the Jews were not allowed in the nicer country clubs in cities across the United States. Jews and black were not allowed so they opened their own clubs.
Almost every major metropolitan city has a Jewish country club that today is accepting of all memberships but again they are private clubs and you have to be sponsored by a member to join.
For instance, in the St. Louis area, the top country clubs did not allow Jews so in the 1910 timeframe they created their own club and it’s still in the top three or four clubs in the St. Louis metropolitan area.