The 'synagogue of satan' as referred to by Christ himself is (modern) code for Freemasonry and Devil Worship: "ye are of your father, the Devil." (Christ)
Jesus was referring to specific pharisee Jews at his time 2000 years ago.
The passages Rev 2 & 3 were written to the Christian churches about false Christians (spiritual Jews) You can read more about the proper understanding here:
Then Jesus went on to warn us about the roman harlot.