You're treating this line like Jesus is saying all Jews and anything of old Israeli culture is automatically evil and satanic.

The part of the bible he quoted says which say they are Jews, and are not, but do lie seems to imply that only those who lie are evil. How did you come to the conclusion that u/LBTrumplican2 is treating (or interpreting) this as all jews, as you claim?

Discernment is key to understanding.

Why does Jesus use this phrase to refer to those who are opposing the mission of the kingdom of God? The name “Satan” means Accuser. And a synagogue was a gathering place. If you put them together, then it is a gathering place of the accuser.

The bible gives more clues as to the identity in Revelations 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 same language is used in Revelations 2:9 for those who are “slandering” and again “say that they are Jews and are not.”

I know your afflictions and your poverty—yet you are rich! I know about the slander of those who say they are Jews and are not, but are a synagogue of Satan.

It's somewhat similar to Paul’s language in Romans 2:28-29

28For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh:

29But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.

Because they are not part of the mission of God, they are no longer to be considered the people of God. You cannot be in direct opposition to Jesus Christ, who is the true Israel, and consider yourself as still being a Jew. You are, as Paul said, only one outwardly.

Anyone involved in slander, lying, accusations or dehumanizing is aligning with Satan's work. While this passage primarily addresses Christian persecution, it extends to all who actively oppose the Kingdom of God and persecute believers, identifying them as part of Satan's work. This would make them a member of the synagogue of Satan.

Matthew 7:15-20

15“Beware of false prophets, who come to you in sheep’s clothing, but inwardly they are ravenous wolves.

16You will know them by their fruits. Do men gather grapes from thornbushes or figs from thistles?

17Even so, every good tree bears good fruit, but a bad tree bears bad fruit.

18A good tree cannot bear bad fruit, nor can a bad tree bear good fruit.

19Every tree that does not bear good fruit is cut down and thrown into the fire.

20Therefore by their fruits you will know them.