I don't think Jesus was huge on the division between church and state. That line in particular was interpreted by his audience to mean they should render no tax to Caesar in Luke.
This item is Caesar's. It has his name on it, his face on it, he made it, it's his. You should return it to him.
You, on the other hand, are God's. You are made in His image, and you should return yourself to Him.
That's why I said "was interpreted by his audience". We know what he (allegedly) said and how his audience (allegedly) understood it. What (if anything) he was implying and whether the audience misunderstood him has been the subject of debate for pretty much the entire history of Christianity.
You can see in the passages directly surrounding what you quote how obvious the Bible makes it. Paraphrasing and injecting context that would have been obvious to the Jewish audiences:
Jews: Should we pay taxes?
Jesus: This item was made by Caesar in the image of Caesar, therefore it's safe to assume it's Caesars property and if he wants it back you should return it to him. But you on the other hand were made in the image of God, you are God's property and you should return to Him.
Jews: Are you the King of the Jews?
Jesus: That is what you have called me.
Jews: This guy says we shouldn't pay taxes and that he's the messiah! Kill him!
Judge: “You brought me this man as one who was misleading the people. And after examining him before you, behold, I did not find this man guilty of any of your charges against him. Neither did Herod, for he sent him back to us. Look, nothing deserving death has been done by him. I will therefore punish and release him.”
Jews: But we really really really really want you to kill him! And we'll probably have an uprising and cause a ton of trouble if you don't!
Judge: Screw it fine, I'll let this other murderer and insurrectionist we had previously held captive go free and crucify Jesus instead.
In the Gospels, only John names the crowd as "Judeans". Mark, Matthew and Luke call them "the crowd", "the mob", or "the people". The people, who were, of course, Judeans, but then remember that so was Jesus, and so where the evangelists, and the other followers of Jesus.
John 18:38 ->
Λέγει αὐτῷ ὁ Πιλᾶτος “Τί ἐστιν ἀλήθεια;” Καὶ τοῦτο εἰπὼν πάλιν ἐξῆλθεν πρὸς τοὺς Ἰουδαίους, καὶ λέγει αὐτοῖς “Ἐγὼ οὐδεμίαν εὑρίσκω ἐν αὐτῷ αἰτίαν.
[Pilate says to him "what is truth?". And having said that he came out again towards the Judeans and says to them "I find no cause in him" ("no cause" meaning: to punish him) .]
https://biblehub.com/texts/john/18-38.htm
Luke 23:18 ->
Ἀνέκραγον δὲ παμπληθεὶ* λέγοντες “Αἶρε τοῦτον, ἀπόλυσον δὲ ἡμῖν τὸν Βαραββᾶν·”
[And the crowd as one cried saying "Take him, and give us Barabbas".]
https://biblehub.com/texts/luke/23-18.htm
Mark 15:11 ->
Οἱ δὲ ἀρχιερεῖς ἀνέσεισαν τὸν ὄχλον ἵνα μᾶλλον τὸν Βαραββᾶν ἀπολύσῃ αὐτοῖς.
[As to the high priests they spurred the mob so that he would rather give back Barabbas to them.]
https://biblehub.com/texts/mark/15-11.htm
Matthew 27:25 ->
Καὶ ἀποκριθεὶς πᾶς ὁ λαὸς εἶπεν “Τὸ αἷμα αὐτοῦ ἐφ’ ἡμᾶς καὶ ἐπὶ τὰ τέκνα ἡμῶν.”
[And in reply the whole people said "His blood on us and on our children".]
https://biblehub.com/texts/matthew/27-25.htm
All of which of course has been interpreted in Christian tradition as "the Jews crucified Christ", and most likely formed the basis for European anti-semitism; the original, and true, anti-semitism. And having read the Gospels it's clear what Jesus himself would have thought of such traditions; how royally pissed off he would have been knowing the hatred that was roused in his name.
The sources you think are helping your point are not, BTW. Which is as one would expect, given your point is basically: "This crowd of people referred to once as Jews, who lived where Jews lived and were interested in the teachings of a Jew who was at that point only talking to Jews and had strong objections to that Jew implying he might be their Jewish-prophesize messiah, those guys? Yeah, that crowd? There's no evidence they were Jews". It's on its face ridiculous, even more with the "evidence" you provide.
> he came out again towards the Judeans and says...
Yes, exactly.
> the chief priests and the elders persuaded the crowd to ask for Barabbas and to have Jesus executed
> the high priests they spurred the mob
Do you think the very small amount of non-Jewish Romans in the area would be interested in the spurring of the Jewish priests and elders?
There's nothing anti-semetic about understanding a historical event as it happened. Do you also think calling for ceasefire in Palestine is also anti-semetic?
I have no ill-will against Jews, I love them as I love all my neighbors. That means I'd stop and provide one food and lodging if I saw they were in need, but I'd share the gospel with them and ask them to repent and join the Kingdom while I was at it. Just as the Lord instructed.
You misunderstand. I didn't accuse you of antisemitism. The point is that neither the evangelists, nor certainly Christ, intended the Jews to be blamed for his crucifixion; οὐ γὰρ οἴδασιν τί ποιοῦσιν.
But, as we say in Greek, my maternal language, όποιος έχει τη μύγα, μυγιάζεται.
If you were to have asked me instead of asserted at me, I'd have said there is no human blame to be placed. The Word took on human form specifically to fulfill the role of the sinless martyr and win over satan, and so He did.
I've heard speculation of demons in the midst of the crowd responsible for guiding the mob, that seems plausible but I do not know of a strong scriptural argument in favor of it.
None of that is to say that it is in any way inaccurate to attribute the words of the Jews to the Jews. This idea that we need to reshape history at every turn in order to not be interpreted as "anti-semeitic" needs to perish.