[Revelation 2:9]I know thy works, and tribulation, and poverty, (but thou art rich) and I know the blasphemy of them which say they are Jews, and are not, but are the synagogue of Satan.
[Revelation 3:9]Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee.
The folks who said they were Jews....and were not, were widely known in the first century as "The Samaritans". These folks were the brothers, fathers and ancestors of Simon Magus. Josephus says in "Antiquities IX, Chapter XIV, Paragraph 3" And when they see the Jews in prosperity, they pretend that they are changed, and allied to them, and call them kinsmen, as though they were derived from Joseph, and had by that means an original alliance with them; but when they see them falling into a low condition, they say they are no way related to them, and that the Jews have no right to expect any kindness or marks of kindred from them, but they declare that they are sojourners, that come from other countries. But of these we shall have a more seasonable opportunity to discourse hereafter.
Josephus make this statement a few more times in his works, so it is quite obvious who the Apostle John was speaking of in Revelation when he talks about those who say they are Jews and are not!
In the letter to the Church at Ephesus,the very first letter to the seven Churches,the people are praised because they drove out those "who said they were apostles but they were not;they lied". Same thing as "those who say they are Jews,but are not:they lie". The caution is to liars,twas then at it is now. Trying to define who was who is not at all the point and one loses sight of Truth when silly word games are pleased. The point is that wolves in sheep's' clothing are dangers,then as now.