Who are these people who say they are Jews, but are not? Jesus also refers to them in His letter to Philadelphia (Revelation 3:9). Remember, these letters are written to the church of God. In His eyes, when there is true faith in Jesus Christ, there is no distinction between Jews and Gentiles. Paul mentions this repeatedly in his epistles (Romans 10:12; Galatians 3:28; Colossians 3:11). "Those who say they are Jews" does not refer to physical descent, as there is no spiritual benefit in being of one race or ethnicity. A church member has no spiritual reason to claim—truly or falsely—to be a physical Jew.
The key to this puzzle is found in Romans 2:28-29:
For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh; but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God.
Applying this to the letters in Revelation, some claim to have a circumcised heart, but they really belong to Satan's assembly. The same situation appears in the Parable of the Wheat and the Tares (Matthew 13:24-30). The wheat and the tares look identical until fruit is produced. At that point, it becomes apparent which is genuine wheat and which is not. Thus, Jesus teaches that we will know people by their fruits (Matthew 7:16-20). Recall also that the workers in the parable are commanded to leave the tares in with the wheat. We see this in Revelation—people with circumcised hearts being troubled by those without them.
In Romans 2:29, Paul provides a trait of those who are converted, and by implication, those who are not. Those with circumcised hearts will have their praise from God. By contrast, those with uncircumcised hearts will seek the praise of men, and what God thinks is an afterthought (see John 12:43). The unconverted are more concerned with the appearance of righteousness before other men than they are with true righteousness before God.
The Pharisees are a good example of this. They made sure that people knew when they were fasting, the frequency and amount of their offerings, and all of their good deeds. They were quite concerned about prestige, honor before men, and the social pecking order. Much of their reasoning process revolved around how things would look or what other people would think. Obviously, these thoughts are not inherently wrong and are often good things to ponder. However, they become wrong when appearance rises higher in priority than righteousness and truthfulness—when it becomes a façade or a pretense.
The members of the Smyrna church, though, are facing persecution because they are more focused on what God thinks than what man thinks. If they sought praise from men—if they wanted to please the people around them—they would not be so readily targeted for persecution. Their beliefs, however, are solid convictions rather than mere preferences, and because carnal man despises the things of God (Romans 8:7), carnal men within—and without—the fellowship persecute them. These pseudo-Jews, as it were, seeking the praise of men rather than God, are verbally cutting down the converted members. Jesus says that He is aware of it—He sees what His people suffer—and He will make it right in His own time.