Let's see what will be pulled from my bag of quotes on the synagogue of Satan!

And unto the angel of the church in Smyrna write; These things saith the first and the last, which was dead, and is alive; 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 2:8-9

Smyrna, greek word for myrrh, a cleansing herb, described the church from ~100-313 AD. Since the beginning, the church was infiltrated and had to be cleansed through its persecution. And at this time (Acts 7 and 10), the Gospel had already been given to the Gentiles:

What shall therefore the lord of the vineyard do? he will come and destroy the husbandmen, and will give the vineyard unto others. Mark 12:9

Be it known therefore unto you, that the salvation of God is sent unto the Gentiles, and that they will hear it. Acts 28:28

Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ. Galatians 3:16

If you belong to Christ, then you are Abraham's seed, and heirs according to the promise. Galations 3:29

and Babylon had already destroyed Jerusalem, to never be rebuilt on earth:

As he approached Jerusalem and saw the city, he wept over it and said, "If you, even you, had only known on this day what would bring you peace-- but now it is hidden from your eyes. The days will come upon you when your enemies will build an embankment again you and encircle you and hem you in on every side. They will dash you to the ground, you and the children within your walls. They will not leave one stone on another, because you did not recognize the time of God's coming to you. Luke 19:41-44

So then what becomes of the term "Jew" in the Bible? Especially pertaining to this time period and beyond?

For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But 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. Romans 2:28-29

For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature. And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God. Galatians 6:15-16

For Q#4379, this is the process of putting on the armor of God; this is sharpening the spear of His word, wielded by the mouth, and splitting darkness asunder.

For many deceivers are entered into the world, who confess not that Jesus Christ is come in the flesh. This is a deceiver and an antichrist. Look to yourselves, that we lose not those things which we have wrought, but that we receive a full reward. Whosoever transgresseth, and abideth not in the doctrine of Christ, hath not God. He that abideth in the doctrine of Christ, he hath both the Father and the Son. If there come any unto you, and bring not this doctrine, receive him not into your house, neither bid him God speed: 2 John 1:7-10

Any nation, or kindred, or tongue that does not knowingly heed this is of the synagogue of Satan.

And the times of this ignorance God winked at; Acts 17:31

Therefore to him that knoweth to do good, and doeth it not, to him it is sin. James 4:17

Let's see what will be pulled from my bag of quotes on the synagogue of Satan!

And unto the angel of the church in Smyrna write; These things saith the first and the last, which was dead, and is alive; 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 2:8-9

Smyrna, greek word for myrrh, a cleansing herb, described the church from ~100-313 AD. Even at its infancy, the church was to be cleansed through its persecution. And at this time (Acts 7 and 10), the Gospel had already been given to the Gentiles:

What shall therefore the lord of the vineyard do? he will come and destroy the husbandmen, and will give the vineyard unto others. Mark 12:9

Be it known therefore unto you, that the salvation of God is sent unto the Gentiles, and that they will hear it. Acts 28:28

Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ. Galatians 3:16

If you belong to Christ, then you are Abraham's seed, and heirs according to the promise. Galations 3:29

and Babylon had already destroyed Jerusalem, to never be rebuilt on earth:

As he approached Jerusalem and saw the city, he wept over it and said, "If you, even you, had only known on this day what would bring you peace-- but now it is hidden from your eyes. The days will come upon you when your enemies will build an embankment again you and encircle you and hem you in on every side. They will dash you to the ground, you and the children within your walls. They will not leave one stone on another, because you did not recognize the time of God's coming to you. Luke 19:41-44

So then what becomes of the term "Jew" in the Bible? Especially pertaining to this time period and beyond?

For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But 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. Romans 2:28-29

For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature. And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God. Galatians 6:15-16

For Q#4379, this is the process of putting on the armor of God; this is sharpening the spear of His word, wielded by the mouth, and splitting darkness asunder.

For many deceivers are entered into the world, who confess not that Jesus Christ is come in the flesh. This is a deceiver and an antichrist. Look to yourselves, that we lose not those things which we have wrought, but that we receive a full reward. Whosoever transgresseth, and abideth not in the doctrine of Christ, hath not God. He that abideth in the doctrine of Christ, he hath both the Father and the Son. If there come any unto you, and bring not this doctrine, receive him not into your house, neither bid him God speed: 2 John 1:7-10

Any nation, or kindred, or tongue that does not knowingly heed this is of the synagogue of Satan.

And the times of this ignorance God winked at; Acts 17:31

Therefore to him that knoweth to do good, and doeth it not, to him it is sin. James 4:17