That doesn't contradict Hebrews 8.
The context of Acts 21 is that there were those among the Jews who were what we'd call Judaizers - that believed perhaps as you do that for Gentiles to become followers of Christ they had to become Jewish.
St Paul strongly disagreed, and emphasized this in his letters over and over. The line - no Jew, no Greek, no male, female, barbarian, Scythian, slave, free is about tribalism and how in Christ there is a new humanity that doesn't operate the way the old humanity does. All the walls of separation between men are broken down. Everything is upside down in Christ, because in Christ - new creation, back to things as they were, just humanity, Adam as a whole, and God. Reunited in the person of Christ Jesus, the new Adam.
St Paul here is being warned that there are people who say he is teaching Jews - not gentiles - to forsake Moses. Is this true? Has St Paul been doing this? No, that is not true.
Neither does this say that St Paul is telling the Gentiles to be circumcised. Here St Luke makes a distinction between what they said about Jews in the diaspora (v20-24) and the Gentiles (v25). Concerning the Gentiles one thing, concerning the Jews another.
Now... see what has happened. They accuse St Paul (wrongly) of brining Trophimus into the temple. (Speaking of wonderful passages of St Paul - in Ephesians 3 he notes that he is "prisoner of Christ Jesus
for you Gentiles...my tribulations for you - this is the event that wound him up in jail).
But Trophimus was a convert! He was a gentile Christian! Now you tell me - a convert who has become Jewish, who follows the Law, who has been circumcised, why would that defile the Temple? And yet the account in Acts makes it clear Trophimus did
not go to the Temple. Why?
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Paul made a Nazarite Vow, with sacrifices in the Temple no less, in order to declare that he was not teaching the Hebrews to forsake the Torah of Moses. If your interpretation of Hebrews is correct, then he's a huge liar. The whole Gospel is all big lie. How can that be?
St Paul was Jew. There was no problem with him keeping the Law. If you're suggesting that Hebrews is evidence of St Paul telling Jews to stop keeping the Law, I can't see it.
I also can't see how the Gospel becomes a lie based on this.
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Not to mention that all the Apostles in Jerusalem seemed to rejoice that people who believed in Yeshau also were zealous for keeping the Law. Will you rebuke James and the other Apostles for this heresy against your doctrine?
No, the Apostles were saying - it's awesome all these Jews have become followers of Christ (those among the Jews who have believed). This is contrasted to his message of those among the Gentiles (v19). But, the caution is that - they are all zealous for the Law. This isn't a doctrinal statement, it's a - hey St Paul, what you've been teaching the Gentiles has been construed that you are converting Jews from the Law, and there are those who are angry about that - so appease them.
I have no problem with Jews keeping the Law. Unfortunately, just as they couldn't sing the songs of Zion in Babylon (How can we sing the songs of the Lord while in a foreign land?) you can't practice Judaism now. The Temple is destroyed. There is no priesthood, there are no sacrifices. There long awaited return of the presence of the Lord to the Temple happened - and they missed it, because it happened in the person of Christ Jesus. The prophet came, the way of the Lord was made straight - and it wasn't to re-establish the Temple or the Jewish rule. They missed it, and people who are trying to do that today are still missing it.
At any rate if we read on, Hebrews 9 clearly says "He is the mediator of a new covenant, so that, death having taken place for redemption of the transgressions under the first covenant, those having been called might receive the promise of the eternal inheritance."
It doesn't matter how you see Acts 21 and Hebrews 8 interrelated. There is no mention of a new priesthood, only a new and living way, a new covenant. It is simply untrue that "new" in 8:13 is referring to the priesthood vs explaining the new covenant prophecy of Jeremiah 31 which was spoken of in just the previous verses!