It is no mere opinion. It is eternal objective truth. Btw, He is both the Lord and the King of the Jews. He has many titles and many names. His view of fake Jews is simple; it's not acceptable in which He will grant them eternal life if they do not worship God the Father and bow to Him, who is the Son of God, the Messiah and the King of Kings. Jesus is the Way, the Life & the Truth. In other words, He means that those who call themselves Jews but prove false will be damned to the Church of the devil aka the Synagogue of Satan unless they seek forgiveness from Jesus Himself. Otherwise, yeah, they are damned for an eternity in Hell. Therefore, today, we see many who'd rather love the things of this world etc which includes serving Satan the Adversary.

To expand on His eternal truth which is not mere opinion to true believers and falsely believed to be opinion by subjective non believers and misguided agnostics, atheists and lukewarm Christians, here is a source to further dig deeper into the meaning of Revelations 3:9.

This is the second time in the letters to the seven churches that the "synagogue of Satan" is mentioned, and the fourth time Satan is referenced (Revelation 2:9; 2:13; 2:24). Apparently, the Jews of Philadelphia, like those of Smyrna, made life hard for the believers in Philadelphia. This is not a blanket reference to all of Judaism, nor all of the Jewish people. Rather, Jesus is indicting a specific group in a specific area. In fact, Jesus said these offenders were Jews in name only. He called them liars. They actually belonged to Satan and served Him.

Perhaps the aggressors tried to force the Christians to be circumcised and to put themselves under the law of Moses, just as Judaizers tried to persuade the churches of Galatia to accept circumcision and submit to the law of Moses (Galatians 1:6–7; 3:1–6). But the Christians at Philadelphia resisted the Judaizers' efforts.

Jesus promised to compel the false Jews to acknowledge the believers' valid faith in Jesus and recognize that Jesus loves the believers. This is most likely a reference to the ultimate victory of good over evil: the day when all false teachers will have to bow to Jesus and confess that He is Lord (Philippians 2:19–11). Christians will witness that triumphant event (Revelation 20:12–15).